Question

Describe how to transform the graph of f(x) = x* to obtain

the graph of the related function g(x) = f(-4(x - 3)) + 1.
Then draw the graph of g(x).

Answer 1

Explanation:

Parent function is, f(x) = x²

For x = -4(x - 3),

f[-4(x - 3)] = [-4(x - 3)]²

= 16(x - 3)²

= 16(x - 3)²

g(x) = 16(x - 3)² is the transformed form of the graph f(x).

Here 16 (Coefficient of x²) represents the vertical stretch of the parent function by 16 units.

Followed by a translation of the function by 3 units right.

Table of input and output values of g(x),

x 0 1 2 3 4 5

y -48 -32 -16 0 16 32

Now plot these points on a graph and join them.