Question

Let f(x)=4x^2+6 .

The function g(x) is f(x) translated 4 units down.



Enter the equation for g(x) in the box.


Let f(x)=3/4x^2−1.

The function g(x) is a vertical stretch of f(x) by a factor of 8.

What is the equation of g(x)?



Enter your answer in the box.

Answer 1

1.) $g(x)=4x^2+2$
2.) $g(x)=3/4x^2+7$

Answer 2

Answer:

1 - $g(x)=4x^2+2$.

2 - $g(x)=6x^2-8$

Step-by-step explanation:

Ques 1: We are given the function, $f(x)=4x^2+6$

Now, we have, the function f(x) is translated 4 units down to get the function g(x).

Thus, the translated function is, $g(x)=4x^2+6-4$.

That is, the translated function is, $g(x)=4x^2+2$.

Ques 2: We are given the function, $f(x)=\frac{3}{4}x^2-1$

Now, we have, the function f(x) is stretched vertically by a factor of 8 to get the function g(x).

Thus, the stretched function is, $g(x)=8\times (\frac{3}{4}x^2-1)$

That is, the stretched function is, $g(x)=6x^2-8$