Exercise 108 Page 93

Practice makes perfect

a The domain is the set of all x-values for which a function is defined. The graph is a parabola and it is the graphs of a quadratic function. Quadratic functions are defined for all values of x.

- ∞ < x < ∞

The range is the set of all y-values the function gives. To help us find the range we can take a look at the graph.

We can see that the graph has its lowest point at (2,3). Therefore, the range does not go below y=3. Outside the region where the graph is drawn, the graph continues to infinity. This means the range is limited to y-values larger than or equal to 3. y ≥ 3 To summarize, we have found that the domain and range are as follows. Domain:& - ∞ < x < ∞ Range:& y ≥ 3

b First, we are going to find the domain, which is the set of all x-values for which the function is defined. For the graph of a cubic function, as with all cubic functions, it is defined for all values of x.

- ∞ < x < ∞

To determine the range of the function, let's look at the graph.

How does the graph continue outside of the drawn area? Since the left-end extends downward and the right-end extends upward, we can deduce from the graph's end behavior that the range is all y-values. - ∞ < x < ∞ We have now found both the domain and range, we can summarize our findings. Domain:& - ∞ < x < ∞ Range:& - ∞ ≤ y < ∞

c Let's start with finding the domain. It is the graph of a quadratic function and is defined for all x-values.

- ∞ < x < ∞ To find the range, we need to look at the graph.

We can see that the graph has its highest point at (- 6, 0). Therefore, the range has an upper limit at y=0. In the coordinate plane, we can see that the graph continues downward outside the drawn region. This means it continues to - ∞. y ≤ 0 Now that both the domain and range have been found we can summarize. Domain:& - ∞ < x < ∞ Range:& y ≤ 0