Example 8: Sketching
Sketch a continuous function 𝑓𝑥 with the following properties:
Decreasing over the interval −∞,−1 
𝑥=1 is a zero of 𝑓𝑥
The average rate of change of 𝑓𝑥 over the interval −3,−1 is −2 
The rate of change of 𝑓𝑥 is decreasing on the interval −∞,−3
𝑓−1 is a relative minimum value.