7. TRANSFORMATIONS: Make a statement that best describes the effects of the graph f(x) = x³ when it is replaced by 2(fx) -5?

Answer 1

Consider the following expression:

a f(b(x+c)) + d

a is vertical stretch/compression.

|a| > 1 stretches

|a| < 1 compresses

a < 0 flips the graph upside down

b is horizontal stretch/compression.

|b| > 1 compresses

|b| < 1 stretches

b < 0 flips the graph left-right

c is horizontal shift.

c < 0 shifts to the right

c > 0 shifts to the left

d is vertical shift.

d > 0 shifts upward

d < 0 shifts downward

The parent function is f(x) = x³. The transformed function is 2f(x) - 5. Another way to express is this 2x³ - 5.

We are seeing a both a vertical stretch by 2 (a = 2; |2| > 1) and a vertical shift downward by 5 (d = -5; -5 < 0).