1. EXAMPLE 1 SOLUTION STEP 1 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. Graph a function of the form y = a x
2. EXAMPLE 1 STEP 3 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 . Graph a function of the form y = a x 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 Domain: x ≥ 0 , Range: y ≥ 0 Vertical stretch by a factor of 2 ANSWER
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
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