Guided Example #1 - Radical Functions

Determine the domain and range of $y = \sqrt{5 - x}$ .

a. Domain: $(- \infty, 5)$ , Range $(0, \infty)$
b. Domain: $(5, \infty)$ , Range $(\sqrt{5}, \infty)$
c. Domain: $(- \infty, 5)$ , Range $[0, \infty)$
d. Domain: $(5, \infty)$ , Range $[\sqrt{5}, \infty)$

The correct answer is C. To see why, view each of the steps below.

Step 1

To answer the question let us analyze the graph of $y = \sqrt{5 - x}$ . First recognize that this function is in the square root family. So its graph is a transformation of the graph of $y = \sqrt{x}$ . The graph of $y = \sqrt{5 - x}$ is a horizontal translation 5 units to the right and then it is reflected in the $y - axis$ .

Step 2

Looking at the graph we can see
that the domain is $(- \infty, 5)$ ,
and range of this function is $[0, \infty)$ .

All Steps

Looking at the graph we can see
that the domain is $(- \infty, 5)$ ,
and range of this function is $[0, \infty)$ .