Question

Which statement is true about the end behavior of the graphed function?

As the x-values go to positive infinity, the function's values go to negative infinity.

As the x-values go to zero, the function's values go to positive infinity.

As the x-values go to negative infinity, the function's values are equal to zero.

As the x-values go to negative infinity, the function's values go to positive infinity.

Answer 1

The correct option is D.

Explanation:

Consider the provided graph of the function.

As the x values go to positive infinity or negative infinity the function value increase or goes to positive infinity.

The end behavior of the function is,

`f(x)\rightarrow +\infty, as x\rightarrow -\infty`

`f(x)\rightarrow +\infty, as x\rightarrow +\infty`

Now consider the provided options.

Option A is incorrect because As the x-values go to positive infinity, the function's values go to positive infinity.

Option B is incorrect because As the x-values go to zero, the function's values doesn't go to positive infinity.

Option C is incorrect because As the x-values go to negative infinity, the function's values are not equal to zero.

Option D is the correct option because As the x-values go to negative infinity, the function's values go to positive infinity.

Therefore, the correct option is D.

Answer 2

Option D (As the x-values go to negative infinity, the function's values go to positive infinity).

Explanation:

The graphed function shows a curve which has two turning points and three x-intercepts, which means it is a cubic polynomial. To check which statement is true, we will check all the statements one by one.

Option A) The graph shows that after the second turning point, the function starts to increase. Which means that as x-values increase, the function values will approach positive infinity. Therefore, option A is incorrect.

Option B) This option is incorrect because the graph explicitly shows that f(0) = 0, which means that when x = 0, the function value is also 0.

Option C) This option is incorrect because the function value is 0 at the x-value = 0, as shown in the graph. It can be also seen that As the x-values go to negative infinity, the function's values go to positive infinity since the value of the function decreases as the value of x decreases. Hence Option D is the correct answer!!!