Question

Using the graph of f(x)=x^2 as a guide, describe the transformations,and then sketch a graph of each functiong(x) = 3x^2

Answer 1

g(x) is a vertical stretch of f(x) by a factor of 3

Step-by-step explanation:

A function g(x) is a vertical stretch of f(x), if g(x) = c*f(x) where c is a number greater than 1.

In this case,

g(x) = 3*f(x) = 3*x²

So, g(x) is a vertical stretch of f(x)

Now, in order to sketch a graph for f(x) and g(x), we are going to use the following table:

x f(x) g(x)

-1 (-1)² = 1 3(-1)² = 3

0 (0)² = 0 3(0)² = 0

1 (1)² = 1 3(1)² = 3

Then, the graph of f(x) and g(x) is: