What transformations change the graph of f(x) to the graph of g(x)?
f(x)=-7x^2 g(x)=-35x^2+5

The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/5 and translated down 5 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5 and translated down 5 units.
The graph of g(x) is the graph of f(x) stretched vertically by a facot of 1/5 and translated up 5 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5 and translated up 5 units.

I think the correct answer from the choices listed above is the last option. The transformation change of the graph of f(x) to the graph of g(x) would be that the graph of g(x) is the graph of f(x) stretched vertically by a factor of 5 and translated up 5 units.

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carlosego carlosego · Answer 2 · 2018-08-08T11:51:59+02:00

For this case we have that the main function is given by:

[tex] f (x) = - 7x ^ 2
[/tex]

We apply the following transformations:

Vertical expansions:

To graph y = a * f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

For a = 5 we have:

[tex] h (x) = 5 * f (x)

h (x) = 5 * (- 7x ^ 2)

h (x) = - 35x ^ 2
[/tex]

Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

For k = 5 we have:

[tex] g (x) = h (x) + k

g (x) = - 35x ^ 2 + 5
[/tex]

Answer:

The graph of g (x) is the graph of f (x) stretched vertically by a factor of 5 and translated up 5 units.