10/5/22 - Combining Transformations

Question 1

What is the standard form of a function with transformations?

Answer 1

g(x) = Af(B(x - h)) + k

Question 2

What is the order of operations for transforming functions?

Answer 2

1. Vertical stretch by A (and vertical reflection if A < 0)
2. Vertical shift by k
3. Horizontal stretch by 1/B and reflection if B < 0
4. Horizontal shift by h

Question 3

In standard form, vertical transformations are written as Af(x) + k and the stretch comes before the shift

In A(f(x) + k), which comes first?

Answer 3

The vertical shift by k because the shifted-up function is modified by A

Question 4

In standard form, horizontal transformations are written as f(B(x - h)) and the stretch comes before the shift

In f(Bx - h), which comes first?

Answer 4

The horizontal shift by h

Question 5

Start with f(x). 1st, shift the graph upward by 2, then do a vertical stretch by 2

What is the equation of the graph?

Answer 5

Shift: f(x) + 2
Shift + stretch: 2[f(x) + 2]

Question 6

When k(t) = 1/(2t + 1)^4, list the parent function and the transformations.

Answer 6

The parent function is p(t) = 1/t^4

p(2t + 1) = 1/(2t + 1)^4
p(2t + 1) = p[2(t + 1/2)]
k(t) = p[2(t + 1/2)]
B = 2, h = -1/2, so there is a horizontal stretch by 1/2 and a horizontal shift by 1/2 units to the left