Given the graph of f(x) above, find the following and write your answers using interval notation (Separate multiple intervals with a comma):
(a) Domain: 7
(b) Range:
(c) Interval(s) on which f(x) is increasing:
(d) Interval(s) on which f(x) is decreasing:
(e) Interval(s) on which f(x) is constant:
(f) Local maxima: 3
(g) Local minima: -5
Answers
Answer:
a) [-9,8)
b) [-5,5]
c) (-4,0), (1,6)
d) [-9,-4), (6,8)
e) [0,1]
f) just the y-value: 5; as a point: (-8,5)
g) just the y-value: -5; as a point: (-4,-5)
Step-by-step explanation:
a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).
b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.
For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.
c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?
d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?
e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?
f) Look for the highest non-infinity point on the graph
g) Look for the lowest non-infinity point on the graph
Related Questions
For the functions f(x) = 2x-5 and g(x) = 3x²-x, find (fog)(x) and (gof)(x).
Answers
The fog(x) of the function will be 6x² -2x - 5 and gof(x) of the function will be 12x² + 62x - 80.
What is the domain of a function?
The collection of values that can be plugged into a function's domain is called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of numbers that the operator assumes is known as its range.
As per the given information in the question,
f(x) = 2x - 5 and,
g(x) = 3x² - x
fog(x) = 2x - 5 and,
gof(x) = 2x - 5
fog(x) = f(g(x))
= f (3x² - x) = 2(3x² - x) -5
= 6x² -2x - 5
gof(x) = g(f(x))
= g (2x - 5) = 3(2x - 5)² + 2x - 5
= 12x² - 75 + 60x + 2x -5
12x² + 62x - 80.
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What is the probability of drawing an odd number or a heart
out of a deck of cards?
Answers
Answer:100/10000000000
Step-by-step explanation:qazwsxeedcrfvtgbyhn
Write a situation that can be represented by 2.5x - 15
Answers
Answer:
Linda starts the month with $15 in debt. Each hour, she makes 2.5 dollars. How many hours will it take for Linda to get out of debt?
A situation that can be represented by the expression 2.5x - 15 is given below.
Let's consider a situation where you are tracking the amount of money you earn from selling handmade crafts. In this scenario, the expression 2.5x - 15 can represent your net earnings after deducting the initial investment and expenses.
Suppose you invest a certain amount of money in materials and supplies to create your crafts. The variable x represents the number of crafts you sell. Each craft generates a profit of $2.50. Therefore, the term 2.5x represents the total profit you earn from selling x crafts.
However, running a business incurs expenses. In this case, the expression -15 represents $15, which is the total expense or cost associated with producing and selling your crafts.
So, 2.5x - 15 calculates your net earnings after subtracting the expenses from the profit. It provides you with a measure of how much money you've made after covering the costs.
By plugging in different values for x, you can evaluate the expression to determine your earnings for various levels of craft sales, allowing you to analyze your profitability and make informed decisions regarding your business.
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I can't figure out this graphing problem, please help!!!
Answers
The equation that represents the graph will be y = - (2)ˣ + 3.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The equation is given below.
y = A · (2)ˣ + k
At x = 0, the value of y is 2.
2 = A + k ...1
At x = 1, the value of y is 1.
1 = 2A + k ...2
Subtract equation 1 from equation 2, then we have
A = -1
Then the value of k is given as,
2 = -1 + k
k = 2 + 1
k = 3
The equation that represents the graph will be y = - (2)ˣ + 3.
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-4 3/4 = x-1 1/5
Whats the value of x
Answers
Answer:3/4 * 1/5 = 3/20 = 0.15
Step-by-step explanation:Multiple: 3/
4 * 1/5 = 3 · 1/4 · 5 = 3/20
Multiply both numerators and denominators. The result fraction keep to the lowest possible denominator GCD(3, 20) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - three quarters multiplied by one-fifth is three twentieths.
help pls asap The polygon circumscribes a circle. What is the perimeter of the polygon?
Answers
Applying the two-tangent theorem, the perimeter of the polygon = 70 cm.
What is the Perimeter of a Polygon?To find the perimeter of a polygon, sum all the side lengths of the polygon all together.
What is the Two-tangent Theorem?If two tangent segment of a circle are drawn to meet at a point outside the circle, the two-tangent theorem says they are congruent together, that is, they have equal length.
Applying the two-tangent theorem, the following side lengths that are missing as labelled in the diagram attached below are:
a = 13 cm
b = 9 cm
c = 5 cm
d = 8 cm
Therefore:
Perimeter of the polygon = 13 + a + b + 9 + 5 + c + d + 8
Plug in the values
Perimeter of the polygon = 13 + 13 + 9 + 9 + 5 + 5 + 8 + 8 = 70 cm.
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PLEASE HELP!!
Two glasses of milk and 3 snack bars have a total of 67 carbohydrates (carbs), and 4 glasses of milk and 2 snack bars have a total of 82 carbs. Determine how many carbs are in one glass of milk and in
one snack bar
There are _____ carbs in one glass of milk
There are _____ carbs in one snack bar
Answers
Answer: The carbs in one glass of milk is 14 carbs and one snack bar is 10 carbs
Step-by-step explanation: Hope this helps!
Answer:
Step-by-step explanation:
78 and 10g
The gcf of 28y-24 is
Answers
Answer:
4
brainliest plssNorthside high school is having a spaghetti dinner funraiser. In order to adveritse, students place flyers on neighborhood doors. Margie hands out 100 flyers in 2 hours. Jaxon hands out 18 flyers in 15 minutes. Which equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours.
A. 18/15 = f/2. B. 120/f = 2/15
C. 18/2 = f/120. D. 120/15 = f/18
Answers
120/15=f/18 is the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
Margie hands out 100 flyers in 2 hours.
Jaxon hands out 18 flyers in 15 minutes.
We need to find the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours.
Let us convert hours to minutes
2 hours=120 minutes.
Let f be the number of flyers Jaxon handed out in 2 hour.
18/15=f/120
Apply cross multiplication
120/f=15/18
120/15=f/18
Hence, 120/15=f/18 is the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours
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A homeowner sections off part of her backyard for a vegetable garden. The width of the garden is 4 ft shorter than the length. The perimeter of the garden is 52 ft. What are the dimensions of the garden?
Answers
Answer:
length = 15ft
width = 11ft
Step-by-step explanation:
p = 2L + 2w = 52ft
w = L - 4
Substitute: 2L + 2(L-4) = 52
Simplify and solve:
2L + 2L - 8 = 52
4L - 8 = 52
4L = 60
L = 15
w = 15-4 = 11
Check:
2(15) + 2(11) = 52?
30 + 22 = 52!!!
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Answers
Answer:
13 years
Step-by-step explanation:
How do we change 0.88 to fraction
Answers
Answer:
22/25
Step-by-step explanation:
0.88 = 88/100
(88:4)/(100:4)
22/25
PLEASE ANSWER ASAP
Beverly is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3). Which TWO slope calculations
can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
Answers
Answer:
Triangle PQR is a right triangle. First we have to find the length of each side of the triangle. This can be done using the points provided, along with the Pythagorean theorem, which is a^2+b^2=c^2. PR^2 = (7- -2)^2+(3-5)^2 = 85 => PR = sqrt(85) QR^2 = (7- -1)^2+(3-1)^2 = 68 => QR = sqrt(68) QP^2 = (1-5)^2+(-1 - -2)^2 =17 => QP = sqrt(17) Now that we have the sides of the triangle, we can put them into the Pythagorean theorem again to see that it works out: (Sqrt(17))^2 + (sqrt(68))^2 = (sqrt(85))^2 17 + 68 = 85 85 = 85 Since the Pythagorean theorem works for right triangles, the triangle is indeed a right triangle.
Step-by-step explanation:
Arturo buys 12 bottles of grapefruit juice at the corner store for a total cost of $8.64. If each bottle costs the same amount, how much is 16 bottles of juice?
Answers
Answer:
[tex]\huge\boxed{\sf \$ \ 11.52}[/tex]
Step-by-step explanation:
Given that,12 bottles of juice = $8.64
Using unitary method.Divide 12 to both sides
12/12 bottle of juice = $8.64/12
1 bottle of juice = $0.72
Multiply 16 to both sides
1 × 16 bottles of juice = $0.72 × 16
16 bottles of juice = $11.52[tex]\rule[225]{225}{2}[/tex]
Find the diameter of the circle.
9 cm
The diameter of the circle is
The solution is I
centimeters.
Answers
The table shows the percent of each type of sandwich a cafe had available on Sunday. Sandwich Percent Ham 35 Roast Beef 25 Turkey 40 There are a total of 225 ham and turkey sandwiches. How many sandwiches did they have in all on Sunday? sandwiches Part B Fill in the blank question. If the cafe sells all the sandwiches at $4.50 each, how much money will the cafe earn?
Answers
The total number of sandwiches they have in all on Sunday is 375 sandwiches.
The amount earned by the cafe if each sandwich cost $4.50 is $1,687.5
What is the total number of sandwiches?Ham sandwich = 35%Roast beef sandwich = 25%Turkey sandwich = 40%Total ham and turkey sandwiches = 225Total number of sandwiches = xTotal percentage of ham and turkey sandwiches = 35% + 25%
= 60%
So,
225 = 60% of x
225 = 0.60 × x
225 = 0.60x
divide both sides by 0.60
x = 225/0.60
x = 375
Hence,
Total number of sandwiches = 375
If the cafe sells all the sandwiches at $4.50 each
The total money earned by the cafe = cost of each sandwich × total number of sandwiches
= $4.50 × 375
= $1,687.5
Therefore, the total sandwiches sold in the cafe on Sunday is 375 sandwiches.
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A medical researcher collects health data on many women in each of several small countries. One of the variables
measured for each woman in the study is her weight in pounds. The following list gives the five-number:
summary for the weights of adult women in one of the countries.
Country A:
92, 110, 120, 160, 240
About what percent of Country A women weigh between 110 and 240 pounds? Show your work.
(a) 50%
(b) 65%
(c) 75%
(d) 85%
(e) 95%
Answers
Option (c) 75% of Country A women weigh between 110 and 240 pounds.
What is the five-number summary?
When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.
Given, the five-number summary of Country A:
92, 110, 120, 160, 240
Then, we get
Minimum value = 92, First quartile = 110, Median = 120, Third quartile=160,
Maximum value = 240
Between 110 and 240 pounds, data lies from the First quartile to Maximum value which represents 75% of the data.
Hence, Option (c) 75% of Country A women weigh between 110 and 240 pounds.
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Solve the absolute value of equation.
List both the answers.
|x|-2=5
Answers
Answer:
-7 or 7
Step-by-step explanation:
|x|-2=5
Add 2 to each side:
|x|=7
Because it is the absolute value, x can be -7 or 7
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2. Give another name for KL
Answers
Answer: Thousand Liters
Step-by-step explanation:
Mr. Clark is contemplating which chauffeured car service to take to the airport. The first costs $28 up front and $1 per kilometer. The second costs $3 plus $2 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the total fare? What is the distance?
Answers
Answer:
The total fare is $53, and the distance is 25
Step-by-step explanation:
The equation we can use for the first car would be:
28 + (1×k) = fare (f)
The equation we can use for the second car would be:
3 + (2×k) = f
If we were to plug in 20 into the equations, it would look like this:
28 + (1×20) = 48 (first car)
3 + (2×20) = 43 (second car)
As you can tell, the prices aren't matched up just yet.
Let's plug 25 into the equations.
28 + (1×25) = 53
3 + (2×25) = 53
The number of kilometers traveled is 25, and the price is $53
11 k x + 12kx= 6 for x
Answers
Answer:
x=1/4k
Step-by-step explanation:
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The required co-terminate angles of 1817° between 0° to 360° is 343°.
What is co-terminal angles?Co-terminal Angles are points who share similar introductory side and terminal sides. Finding co-terminal points is just about as straightforward as adding or taking away 360° or 2π to each point, contingent upon whether the given point is in degrees or radians. There are a boundless number of co-terminal Angles that can be found.
According to question:For calculating co-terminal of angle 1817°,
We will subtract given angle 1817° from 2160°(multiple of 360°)
Then,
2160° - 1817°
343°
Thus, the co-terminating angle of 1817° is 343°.
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UNIT 3
FORM B continued
UNIT JASSESSMENT
●
Name:
3 Simon and Reina practice basketball shots. Simon makes 7 baskets for every S
misses. Reina makes 9 baskets for every 7 misses. Who makes a basket more often?
Show your work.
Answers
The person who makes a basket more often, between Simon and Reina, is Simon
How to find who makes more baskets ?To find who makes the basket more, you need to find the percentage number of times the basket is made.
The percentage number of times the basket is made by Simon is :
= Number of baskets made / ( Number of baskets made + Number of baskets missed ) x 100 %
= 7 / ( 7 + 5 ) x 100%
= 7 / 12 x 100%
= 58.3%
The percentage number of times Reina makes the basket is :
= 9 / ( 9 + 7 ) x 100%
= 9 / 16 x 100%
= 56.25%
Simon therefore makes the basket more.
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Will this summer be especially hot? The Farmer's Almanac is calling for a particularly hot summer this year. A student would like to estimate the average temperature using a thermometer that she places outside. Prior to the start of summer, the student randomly selects 10 days that she will use as her sample. On each of those 10 days, she records the outside temperature at 3 p.m. Assume that all conditions for inference have been met. (a) After collecting her data, the student calculates a 95% confidence interval to estimate the population mean. In this case, what is the population? the temperature all days for that summer the time of the day the 10 days (b) Suppose the calculated confidence interval is (72, 88) degrees Fahrenheit. What is the value of the point estimate (in degees Fahrenheit)? °F (c) Based upon your calculated point estimate and the confidence interval given in Part (b), what is the estimated margin of error (in degees Fahrenheit)? °F
Answers
a) The population of the confidence interval is given as follows: The temperature all days for that summer.
b) The point estimate of the interval is of: 80 degrees Fahrenheit.
c) The margin of error of the interval is of: 8 degrees Fahrenheit.
What are the features of the confidence interval?A confidence interval for a population parameter is built taking a sample of this population.
Then, the interval for the population mean is given as the sample mean plus/minus the margin of error.
The sample in this problem is given as follows:
The temperature for 10 days of summer.
Hence the population is of:
The temperature all days for that summer.
The interval in this problem is given as follows:
(72, 88).
The point estimate is the mean of the bounds, hence:
Point estimate = (72 + 88)/2 = 80.
The margin of error is half the difference of the two bounds, hence:
Margin of error = (88 - 72)/2 = 8.
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- Adult male Florida panthers have an
average weight of 52.6 kg. What is the
average weight of a male Florida panther
rounded to the nearest whole number?
Answers
The average weight of a male Florida panther rounded to the nearest whole number is 53 kg
What is average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
Average weight = 52.6 kg
52.6
The number after decimal point is 6 which is more than 5.
So add 1 to the 52, we get 53
Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg
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3. The lines represented by the equations
6y +4x = 12 and 3y + 2x = 21 are
A. parallel
B. the same line
C. perpendicular
D. neither parallel nor perpendicular
Answers
geomerty help please
Answers
Answer:
y = 10, x = 18
Step-by-step explanation:
Hope it helps!
Will give brainliest
Answers
Answer:
The function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x
Step-by-step explanation:
Transformation techniques
Transformation is the process of changing the position of an object on the xy-plane.Given the parent functionf(x) = 4xIf the function is not reflected over x-axis, the resulting function will be f(x) = -4xIf the resulting function is compressed by a factors of 1/8, hence the final function rule will be;g(x) = 1/8(-4x)g(x) = -1/2xHence the function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x
Hope this helps!
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Which ordered pair would make this set a function when it replaces (x, y)?
{(0, 1), (2, 6), (1, 7), (5, 7), (x, y)}
ANSWER CHOICES
(2, 4)
(5, 9)
(1, 6)
(4, 8)
Answers
Answer:
Step-by-step explanation:
(4,8)..Its the only one in which x doesnt repeat
John's bank account was overdrawn. The status of his account was -107. He did not realize the problem and wrote another check for $43. The bank charged him a $22 fee for being overdrawn.
Answers
Answer: -$155
Step-by-step explanation:
Using this formula
New status=(-Account status-Cheque amount)-Bank charges
Let plug in the formula
New status= (-$112-$22)-$21-
New status=-$134-$21
New status=-$155
Inconclusion The new status of John's account at this point is -$155
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