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

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 323 People

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.

Answered by maham237 @ 26/12/2020

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

$f (x) = - 7x ^ 2$

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:

$h (x) = 5 * f (x)\\h (x) = 5 * (- 7x ^ 2)\\h (x) = - 35x ^ 2$

Vertical translations:

Suppose that k> 0

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

For k = 5 we have:

$g (x) = h (x) + k\\g (x) = - 35x ^ 2 + 5$

Answer:

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

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

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