Question

Without graphing, describe the transformation from the parent function

f(x) = | x |.

1. y = 5| x |
2. y = 1/3 I x I
3. y = 3| x |

Answer 1

1. y = 5|x| ⇒vertical stretch

2. y = ⅓|x| ⇒vertical compression

3. y = 3|x| ⇒vertical stretch

Explanation:

Given the parent absolute value function, f(x) = |x|:

1) y = 5|x|

The transformed function, y = a|x|, where |a| > 1, represents the vertical stretch of the parent graph by a factor of a.

• A vertical stretch is a transformation to the parent function where there is an increase in distance between corresponding points of a graph.

Therefore, the absolute value equation, y = 5|x|, represents a vertical stretch of the parent function by a factor of 5. The graph of y = 5|x| is narrower than the parent function, f(x) = |x|.

2) y = ⅓|x|

The transformed function, y = a|x|, where 0< |a| < 1, represents the vertical compression of the parent graph by a factor of a.

• A vertical compression is a transformation to the parent function where there is a decrease in distance between corresponding points of a graph.

Therefore, the absolute value equation, y = ⅓|x|, represents a vertical stretch of the parent function by a factor of ⅓. The graph of y = ⅓|x| is wider than the parent function, f(x) = |x|.

3) y = 3|x|

Similar to question 1, the absolute value equation, y = 3|x|, represents a vertical stretch of the parent function by a factor of 3. The graph of y = 3|x| is narrower than the parent function, f(x) = |x|.

Attached are the graphs of the given absolute value functions, where it shows the transformations to the parent function, f(x) = |x|.