The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an
equation for the stretched or compressed graph.
-$y = x ^ { 2 } - 1 \quad$ stretched horizontally by a factor of 4
A) $y = \frac { x ^ { 2 } } { 4 } - 1$
B) $y = 16 x ^ { 2 } - 1$
C) $y = \frac { x ^ { 2 } } { 16 } - 1$
D) $y = 4 x ^ { 2 } - 4$

Question

Quizplus · Accepted Answer

When a function is stretched or compressed horizontally by a factor of $a$, the stretch or compression is along the $x$-axis, and the graph is compressed by a factor of $a$ when $a>1$, and stretched by a factor of $\frac{1}{a}$ when $0<a<1$. So, when the graph is stretched horizontally by a factor of $4$, the equation becomes $y=\frac{x^2}{(4)^2}-1$, which simplifies to $y=\frac{x^2}{16}-1$. Therefore, the best choice is $\boxed{	extbf{(C)}}.$

The Problem Tells by What Factor and Direction the Graph y=x2−1y = x ^ { 2 } - 1 \quady=x2−1

The Problem Tells by What Factor and Direction the Graph $y = x ^ { 2 } - 1 \quad$