This lesson covers analyzing the graphs shown for Explore (Which One Doesn’t Belong). Start with the analysis of the graph of the absolute value function shown below.
*Graphs are created using Desmos.com.
When analyzing absolute value functions the following characteristics must be determined.
- Is the graph an absolute value function? If yes, answer the following:
- What is the axis of symmetry \(x=h\)?
- What is the vertical shift \(k\)?
- What is the vertex \((h,k)\)?
- What is the dilation factor and orientation \(a\) from the vertex?
- What is the equation \(y=a|x-h|+k\)?
For this example, the graph represents an absolute value function with the following characteristics:
- The axis of symmetry is \(x=-3\).
- The vertical shift is \(k=-1\).
- The vertex is \((-3,-1)\).
- The dilation is 2 (over 1 and down 2, over 2 and down 4, etc.) and the orientation (opens down) gives \(a=-2\).
- The equation is \(y=-2|x+3|-1\).
Analyze each graph below from Explore (Which One Doesn’t Belong).
- Graph 1: Red
- Graph 2: Blue
- Graph 3: Green
- Graph 4: Orange
Check Your Analysis
