Question

Determine the end behavior for each function below. Place the letter(s) of the appropriatestatement(s) on the line provided. A. As x approaches ∞o, y approaches ∞oB. As x approaches -œo, y approaches œC. As x approaches ∞o, y approaches -∞0D. As x approaches -c0, y approaches -00

Answer 1

Solution:

From the given graphs,

The first graph is the absolute function graph.

Which can be expressed in the form

$y=-|x|$

Since the leading coefficient is negative,

The end behavior of the graph is

$As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow-\infty$

Hence, the answers are C and D

The second graph is a quadratic graph of the form

$y=x^2$

Since the leading coefficient is positive

The end behavior will be

$As\text{ x}\rightarrow\infty,y\rightarrow\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty$

Hence, the answers are A and B

The third graph is a cubic function that can be expressed in the form

$y=-x^3$

The leading coefficient is negative.

The end behavior will be

$As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty$

Hence, the answers are C and B