Examine the function $y=g(x)$ graphed at right.

1. Which $x$-values have points on the graph? That is, describe the domain of $g$.

   Answer (a):

   The domain includes $-2, 4$ and all the numbers between. $-2 ≤ x ≤ 4$.

2. What are the possible outputs for $g(x)$? That is, what is the range?

   Answer (b):

   The range includes $-1,3$, and all the numbers between. $-1 ≤ y ≤ 3$.

3. Ricky thinks the range of $g(x)$ is $–1, 0, 1, 2,$ and $3$. Is he correct? Why or why not?

   Hint (c):

   Is there a point on the graph for $x = 2.5?$ or for $x = -0.33?$

   Answer (c):

   He is not correct since he is missing all the values between his numbers.
   The curve is continuous, so the description needs to include all numbers, not just integers.

4. Make a sketch of another function with the same domain and range as $g$.

   Answer (d):

   There are many possibilities. Here is one example.