Exercise 1 Page 325

If we know how the function moves around these points, we get an idea of what it looks like. In order to do that, we can calculate the h-values of the following intervals. Note that h represents the function's values for different values of x. x&<- 6 - 6< x& < 7 7< x& Let's choose some arbitrary x-values in these intervals and find their corresponding h-values.

With the possible exception of the y-intercept, the actual h-values for the given x-values we used are not important. Instead, we are more interested if the function is above or below the x-axis in the given intervals. This will tell us how the function grows, which we can use to sketch the graph. h(- 7)&= 14 &&⇒ Abovethex-axis h(0)&= - 42 &&⇒ Belowthex-axis h(8)& = 14 &&⇒ Abovethex-axis Going from above to below the x-axis means that the function is decreasing, and vice-versa. We will sketch the graph so that it intercepts the y-axis at (0,- 42). Adding the obtained points to the diagram will help to make a better sketch.

Now let's graph the function on our graphing calculator and compare. Notice that we can use the same window-setting as in our sketch to make sure the proportions are the same.

The graphing calculator image is very similar to our graph.