10/5/22 - Horizontal Transformations

Question 1

Which coordinates do horizontal transformations change?

Answer 1

x-coordinates

Question 2

How do you represent a horizontal reflection?

Answer 2

If f(x) is a function, then f(-x) is its horizontal reflection. The graph is reflected across the y-axis.

Question 3

How do you represent a horizontal stretch?

Answer 3

f(Bx), where B is a constant

Question 4

f(4x) is a horizontal stretch by ____

Answer 4

1/4

Question 5

f(1/2 x) is a horizontal stretch by ____

Answer 5

2

Question 6

How do you graph a horizontal stretch f(Bx)?

Answer 6

Pick points on f(x) and multiply the x-coordinates by 1/B

Question 7

How do you represent a horizontal shift?

Answer 7

f(x - h)
If h is positive, it’s a shift to the right
If h is negative, it’s a shift to the left

Question 8

Describe the horizontal shift in f(x - 3)

Answer 8

3 units to the right

Question 9

Describe the horizontal shift in f(x + 8)

Answer 9

8 units to the left

Question 10

How do you graph a horizontal shift f(x - h)?

Answer 10

Pick points on f(x) and add h to the x-coordinates

Question 11

If you have the graph of f(x) how do you graph f(2x + 2)?

Answer 11

1. Write it as f(2(x + 1)), B = 2, h = -1
2. Do a vertical stretch by 1/B or 1/2. Multiply x-coordinates by 1/2.
3. Do a vertical shift by h or -1. Subtract 1 from the x-coordinates. The graph is shifted 1 unit left.