Question

f(x)=2|x - 4|
for each circled number in the picture, use the drop - down option below to select the transformation it causes to the graph.

1. select answer
2. select answer

Explanation:

Step1: Analyze the coefficient of the absolute - value function

The general form of an absolute - value function is $y = a|x - h|+k$. In the function $f(x)=2|x - 4|$, the coefficient $a = 2$. When $|a|>1$, the graph of $y = |x|$ is vertically stretched. Here, the factor of vertical stretch is 2. So, the circled number 1 (the coefficient 2) causes a vertical stretch by a factor of 2 to the graph of the parent absolute - value function $y = |x|$.

Step2: Analyze the value inside the absolute - value

For the function $f(x)=2|x - 4|$, the value of $h = 4$ in the general form $y=a|x - h|+k$. When $h>0$, the graph of $y = a|x|$ is shifted to the right by $h$ units. So, the circled number 2 (the value 4 inside the absolute - value) causes a horizontal shift 4 units to the right of the graph of the parent absolute - value function $y = |x|$.

Answer:

1. Vertical stretch by a factor of 2
2. Horizontal shift 4 units to the right