Select the correct answer.

the graph of function f is shown.

function g is represented by the table.

x: -2, -1 , 0, 1, 2
g(x): -2/3, 0, 2, 8, 26

which statement correctly compares the two functions?

a. they have the same x-intercept and the same end behavior as x approaches ∞.

b. they have the same x- and y-intercepts.

c. they have the same y-intercept and the same end behavior as x approaches ∞.

d. they have different x- and y-intercepts but the same end behavior as x approaches ∞.

  C. They have the same y-intercept and the same end behavior as x approaches ∞

Step-by-step explanation:

Both appear to be exponential functions, so will have the same end behavior as x approaches ∞.

The y-intercept on the graph is 2, as it is in the g(x) table.

The x-intercept on the graph is near -2, but it is -1 in the table.

So, the x-intercepts are different, the y-intercepts are the same, and the end behavior is the same.

_____

The growth factor for g(x) appears to be larger. The graph represents g(x) (black) and f(x) (red). The given table values are shown as green points.

For the given functions f(x) and g(x) the statement  that compares both of them correctly is given by option C from the following options

C. They have the same y-intercept and the same end behavior as x approaches ∞.

option C correctly compares the two functions.

According to the language of the question for function g(x)

x: -2, -1 , 0, 1, 2

g(x): -2/3, 0, 2, 8, 26

The graph of function g(x) is attached.

We can clearly see that when g(x) =0  , the value of x is -1

It means that the x intercept of the function g(x) is -1.

Also at x =0 , g(x) = 2  so the y intercept of   g(x) is 2.

Also the given graph is of function f(x) and the value of y intercept is 2 and value of x intercept for f(x) is -2 .

y intercept of f(x) = y intercept of g(x) = 2

We have to identify that out of the given options  which statement correctly compares the two functions

The options are given below

A. They have the same x-intercept and the same end behavior as x approaches ∞.

B. They have the same x and y-intercepts.

C. They have the same y-intercept and the same end behavior as x approaches ∞.

D. They have different x and y-intercepts but the same end behavior as x approaches ∞.

From the graph attached for function g(x) we can see that the nature of function g(x) is similar to exponential function and the given function f(x) also seem to be exponential function by its graph.

So their end behavior will be same as x approaches to .

So we can conclude from the above given facts that option C is correct .

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