Question

The graph of h(x) = x² was transformed to create the graph of k(x) = -1/7x²? Which of these describes the transformation from the graph of h to the graph of k?
A.) A reflection over the x-axls and a vertical stretch
B.) A reflection over the x-axis and a vertical compression
C.) A reflection over the y-axis and a vertical compression
D.) A reflection over the y-axis and a vertical stretch

Answer 1

Given:

The functions are:

$h(x)=x^2$

$k(x)=-\dfrac{1}{7}x^2$

To find:

The transformation from the graph of h to the graph of k.

Solution:

The transformation is defined as

$k(x)=ah(x+a)=$                .... (1)

Where, a is stretch factor

If 0<|a|<1, then the graph compressed vertically by factor |a| and if |a|>1, then the graph stretch vertically by factor |a|.

If $a$, then the graph of h(x) reflected across the x-axis.

We have,

$h(x)=x^2$

$k(x)=-\dfrac{1}{7}x^2$

It can be written as

$k(x)=-\dfrac{1}{7}h(x)$         ...(2)

On comparing (1) and (2), we get

$a=-\dfrac{1}{7}$

The graph of h(x) reflected across the x-axis.

$|a|=\dfrac{1}{7}$

So, the graph is compressed vertically.

It means the graph of h reflection over the x-axls and a vertical stretch to get the graph of k.

Therefore, the correct option is B.