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# Sketching Polynomial Functions

## Exercise 1.5 - Solution

a

You know that a function is increasing if its -value increases when moving to the right along the -axis, and that it is decreasing if its -value decreases. Based on this, highlight where the function increases and decreases.

The function is decreasing up until and then it starts to increasing. Let's write these as intervals.

Interval Increasing/Decreasing
Decreasing
Increasing
b

Let's do as in the previous part. We see that the function is increasing up to After that, it starts to decrease. It decreases until where it starts to increase in value once more.

Let's write this as intervals.

Interval Increasing/Decreasing
Increasing
Decreasing
Increasing
c

The graph shown in the diagram is a linear function, which means the function is either increasing or decreasing for all values of This function, in particular, is increasing, since it has a positive slope. That means the -values get larger for each increasing value of