1. EXAMPLE 1 SOLUTION STEP 1 Graph a function of the form y = a x Graph the function y = 3 x and identify its domain and range. Compare the graph with the graph of y = x. Make a table. Because the square root of a negative number is undefined, x must be nonnegative. So, the domain is x ≥ 0. STEP 2 Plot the points.

2. EXAMPLE 1 STEP 3 Graph a function of the form y = a x STEP 4 Draw a smooth curve through the points. From either the table or the graph, you can see the range of the function is y ≥ 0. Compare the graph with the graph of y = x. The graph of y = 3 x is a vertical stretch (by a factor of 3 ) of the graph of y = x.

3. EXAMPLE 2 Graph a function of the form y = a x SOLUTION Graph the function y = –0.5 x and identify its domain and range. Compare the graph with the graph of y = x. To graph the function, make a table, plot the points, and draw a smooth curve through the points. The domain is x ≥ 0. The range is y ≤ 0.The graph of y = –0.5 x is a vertical shrink (by a factor of 0.5 ) with a reflection in the x- axis of the graph of y = x.

4. EXAMPLE 3 Graph a function of the form y = x + k SOLUTION Graph the function y = x + 2 and identify its domain and range. Compare the graph with the graph of y = x. To graph the function, make a table, then plot and connect the points. The domain is x ≥ 0. The range is y ≥ 2.The graph of y = x + 2 is a vertical translation (of 2 units up) of the graph of y = x.

5. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 1. y = 2 x ANSWER Domain: x ≥ 0, Range: y ≥ 0 Vertical stretch by a factor of 2

6. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 2. y = –2 x Domain: x ≥ 0, Range: y ≤ 0 Vertical stretch by a factor of 2 and a reflection in the x -axis ANSWER

7. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 3. y = x– 1 Domain: x ≥ 0, Range: y ≥ 0 – 1 Vertical translation of 1 unit down ANSWER

8. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 4. y = x+ 3 Domain: x ≥ 0, Range: y ≤ 0 Vertical translation of 3 units up ANSWER