How do you find the equation of each function? Function A is f(x)=3x^2 and Function C is f(x)=18x-16. How do you get those? And then how do you get the equation for Function B? Thanks!

Answer:

[tex]f(x) = 3^x[/tex] --- Function A

[tex]f(x) = x^2 - 5[/tex] --- Function B

[tex]f(x) = 18x -6[/tex] --- Function C

Step-by-step explanation:

Solving (a): Equation of Function A

An exponential equation is represented as:

[tex]y = ab^x[/tex]

From the graph of function A,

[tex]x = 0\ when\ y = 1[/tex]

[tex]x = 1\ when\ y = 3[/tex]

For: [tex]x = 0\ when\ y = 1[/tex]

[tex]y = ab^x[/tex] becomes

[tex]1 = ab^0[/tex]

[tex]1 = a[/tex]

[tex]a =1[/tex]

For: [tex]x = 1\ when\ y = 3[/tex]

[tex]y = ab^x[/tex] becomes

[tex]3 = a*b^1[/tex]

[tex]3 = a*b[/tex]

Substitute 1 for a

[tex]3 = 1*b[/tex]

[tex]3 = b[/tex]

[tex]b = 3[/tex]

[tex]y = ab^x[/tex] becomes

[tex]y = 1*3^x[/tex]

[tex]y = 3^x[/tex]

Replace y with f(x)

[tex]f(x) = 3^x[/tex]

Solving (b): Equation of Function B

A quadratic equation is represented as:

[tex]y = ax^2 + bx + c[/tex]

From the table of function B,

[tex]x = 3\ when\ y =4[/tex]

[tex]x = 5\ when\ y =20[/tex]

[tex]x = 6\ when\ y =31[/tex]

For: [tex]x = 3\ when\ y =4[/tex]

[tex]y = ax^2 + bx + c[/tex] becomes

[tex]4 = a*3^2 + b*3 + c[/tex]

[tex]4 = a*9 + 3b + c[/tex]

[tex]4 = 9a + 3b + c[/tex]

For [tex]x = 5\ when\ y =20[/tex]

[tex]y = ax^2 + bx + c[/tex] becomes

[tex]20 = a*5^2 + b*5 + c[/tex]

[tex]20 = a*25 + b*5 + c[/tex]

[tex]20 = 25a + 5b + c[/tex]

For [tex]x = 6\ when\ y =31[/tex]

[tex]y = ax^2 + bx + c[/tex] becomes

[tex]31 = a*6^2 + b*6 + c[/tex]

[tex]31 = a*36 + b*6 + c[/tex]

[tex]31 = 36a + 6b + c[/tex]

So, we solve for a, b and c in:

[tex]4 = 9a + 3b + c[/tex]

[tex]20 = 25a + 5b + c[/tex]

[tex]31 = 36a + 6b + c[/tex]

Make c the subject in [tex]4 = 9a + 3b + c[/tex]

[tex]c = 4 - 9a - 3b[/tex]

Substitute [tex]c = 4 - 9a - 3b[/tex] in [tex]20 = 25a + 5b + c[/tex] and [tex]31 = 36a + 6b + c[/tex]

[tex]20 = 25a + 5b + c[/tex] becomes

[tex]20 = 25a + 5b + 4-9a-3b[/tex]

Collect Like Terms

[tex]-4+20 = 25a -9a+ 5b -3b[/tex]

[tex]16 = 16a+ 2b[/tex]

Divide through by 2

[tex]8 = 8a + b[/tex]

[tex]c = 4 - 9a - 3b[/tex]

[tex]31 = 36a + 6b + c[/tex] becomes

[tex]31 = 36a + 6b + 4 - 9a - 3b[/tex]

Collect Like Terms

[tex]-4+31 = 36a - 9a+ 6b - 3b[/tex]

[tex]27 = 27a+ 3b[/tex]

Divide through by 3

[tex]9 = 9a + b[/tex]

Solve for a and b in: [tex]8 = 8a + b[/tex] and [tex]9 = 9a + b[/tex]

Subtract both equations:

[tex]8 - 9 = 8a - 9a + b - b[/tex]

[tex]8 - 9 = 8a - 9a[/tex]

[tex]-1 = -a[/tex]

Divide both sides by -1

[tex]1 = a[/tex]

[tex]a = 1[/tex]

Substitute 1 for a in [tex]9 = 9a + b[/tex]

[tex]9 = 9*1 + b[/tex]

[tex]9 = 9 +b[/tex]

Subtract 9 from both sides

[tex]9-9=9-9+b[/tex]

[tex]0=b[/tex]

[tex]b = 0[/tex]

Substitute [tex]b = 0[/tex] and [tex]a = 1[/tex] in [tex]c = 4 - 9a - 3b[/tex]

[tex]c = 4 - 9*1-3*0[/tex]

[tex]c = 4 - 9-0[/tex]

[tex]c = -5[/tex]

So, the equation is:

[tex]y = ax^2 + bx + c[/tex]

[tex]y=1*x^2 +0*x-5[/tex]

[tex]y=x^2 -5[/tex]

Replace y with f(x)

[tex]f(x) = x^2 - 5[/tex]

Solving (c): Equation of Function C

This is calculated using:

[tex]f(x) =a + (x -1)d[/tex]

Where

[tex]a = 12[/tex] -- the first term

d = the difference between successive terms

[tex]d = 30 -12 = 48-30 = 66 -48[/tex]

[tex]d =18[/tex]

So, we have:

[tex]f(x) =a + (x -1)d[/tex]

[tex]f(x) = 12 + (x - 1)*18[/tex]

Open bracket

[tex]f(x) = 12 + 18x - 18[/tex]

Collect Like Terms

[tex]f(x) = 18x - 18+12[/tex]

[tex]f(x) = 18x -6[/tex]

For every 2 cars you wash, your friend washes 3 cars. You wash a total of 8 cars. Complete the table to show the number of cars your friend washes.

The quantity of 7 less than x, multiplied by 4

MUST ANSWER BOTH QUESTIONS FROM ATTACHMENT.
WILL GIVE BRAINLEST
IM ON A TIME LIMIT BY THE WAY

Giving brainliest!!!!!!!!!!!!

Which of the following is equivalent to 2 2/5 ?

1 7/5
1 12/5
1 6/5
1 9/5

i choose 1 7/5 is this correct?

help solve, thank you much yall

Write a summary of the poem "Revenge"

helppppppppppppppppppppp​

Louis wants to carpet the rectangular floor of his basement. The basement has an area of 2,880 square feet. The width of the basement is

4

5

its length.What is the length of Louis's basement?? Please help! i gotta turn this in TODAY!

3. Use powers to rewrite these problems:

a. y y y y y y

b. 7 * 7 * 7 * 7 * n n n n n * m

c. y y * y y

d. t * t * t * t

URGENT HELP

I don’t understand the question can someone please explain how to get answer

Math homework dfmtikjekrjtkttotyy

This my last question my bad guys and I appreciate everybody that’s been helping me out!!!❤️

How many times do you need to multiply by ten to get from 0.35 to 35?

Two schools are 646 meters from each other. On a map, the two schools are 8.5 centimeters apart.
What scale is the map using?

I dont know how to solve this

If right mark brainlest I wanna pass please ' '
0 0
w

For breakfast, Tyrell can choose from scrambled eggs or an omelette, bacon or sausage and orange juice or milk. How many different outcomes are possible

Help me please and thank you! its due and this is the last question...

I need help please
1) The number of fish in a pond can be modeled by the function f(t)=1200(0.85)^t, where t is the number of years. Which of the following is true?

A. The fish population increases by 85% each year.

B. The fish population decreases by 85% each year.

C. The fish population decreases by 15% each year.

D. The fish population increases by 15% each year.

For a loan of $40,000 at 12% for 10 years, how much do you wind up paying back?

80,000
48,000
88,000
8,000

The adult height of a male is about 1.19 times his height at age 12. The adult height of a female is about 1.07 times her height at age 12. Predict how tall is Miguel and Ramona will be as adults if Miguel is 1.5 m and Ramona is 1.6 m. Predict how tall you will be.

Pls help me I don't understand how to get how yall I will be and I think I did the first part right but not too sure.