Question

The graph of the cubic parent function is reflected across the x-axis. Which of the following describes the end behaviorof the new function as x approaches negative infinity?Select one:O a. f(x) approaches negative infinity.O b. f(x) approaches positive infinity.O c. f(x) approaches 0.O d. f(x) approaches 3.

Answer 1

Solution:

A cubic parent function is given below;

$y=x^3$

A cubic parent function is graphed as shown;

Cubic functions are functions with a degree of 3, which is odd. Functions with odd degrees have opposite end behaviors.

The format of writing this is:

$\begin{gathered} x\rightarrow\infty,f(x)\rightarrow\infty \\ As\text{ x tends towards positive infinity, f(x) tends towards positive infinity.} \\ \\ \\ \text{Also,} \\ x\rightarrow-\infty,f(x)\rightarrow-\infty \\ As\text{ x tends towards negative infinity, f(x) tends towards negative infinity.} \end{gathered}$

However, the new function was said to be reflected across the x-axis.

The reflected function is given by;

$y=-(x^3)$

The graph is as shown below;

The end behavior of the new function will now be;

$\begin{gathered} x\rightarrow\infty,f(x)\rightarrow-\infty \\ As\text{ x tends towards positive infinity, f(x) tends towards negative infinity.} \\ \\ \\ \text{Also,} \\ x\rightarrow-\infty,f(x)\rightarrow\infty \\ As\text{ x tends towards negative infinity, f(x) tends towards positive infinity.} \end{gathered}$

Therefore, the answer is option B for the new function