80 points!!! Which equation represents f(x)?
Of(x) = -
O f(x) = -3/x-1
O f(x) = -x-1
O f(x) = -x

Some times it's really very easy to answer the problem just by looking over the given problem.

For the given graph, we need to observe some(or any) point on the graph that can conclude anything to answer the given problem.

Generally we observe x or y-intercepts of the graph first.

Let us observe the y-intercept of the given graph, because we can see a clear picture of y-intercept there.

By looking on the graph, we can see y-intercept is at -1.

Note: y-intercept is a point on y-axis where value of x is 0.

Now let us observe the given functions in the given options.

First option: If we plug x=0 in the given function, we get f(0)=0.

So, y-intercept for first option is 0.

Second option: If we plug x=0, we get a negative -1 inside radical. Cube root of -1 is -1. On multiplying by -1 we get +1.

So, y-intercept for second option is 1.

Third option : If we plug x=0 in that function, we get 0-1 = -1.

So, the y-intercept for third function is -1.

Therefore, function in third option is the correct function for given graph.

Therefore, third option [tex]f (x) = \sqrt[3]{-x} -1[/tex] is correct option.

F(x) =  ∛-x   -1

A polynomial equation with a 3-exponent greatest exponent is called a cubic equation. Despite having many more uses for understanding more complex mathematics, such as calculus, cubic equations are frequently employed to calculate volumes.

Given a graph of a cubic function for calculating the cubic function we need to standardize it. since it's a single aggregate graph that standard function would be.

x = a(y + 1 )³

for the value y tends to -1. "a" will be  -1.

Hence,

x = -1 (y+1)³

(y + 1 )³ =  -x

y+1  =  ∛-x

y = ∛-x   -1

Therefore, for the given graph F(x) = y = ∛-x   -1.

Learn more about cubic function here:

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