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Verdich [7]
3 years ago
12

The graph of h(x) = x² was transformed to create the graph of k(x) = -1/7x²? Which of these describes the transformation from th

e 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
Mathematics
1 answer:
saw5 [17]3 years ago
6 0

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 <em>h</em> reflection over the x-axls and a vertical stretch to get the graph of <em>k.</em>

Therefore, the correct option is B.

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