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Alg1 ch1101example45
1. EXAMPLE 4 SOLUTION Graph the function y = x â 4 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. To find the domain, find the values of x for which the radicand, x â 4 , is nonnegative. The domain is x â„ 4 . Graph a function of the form y = x â h
2. EXAMPLE 4 Graph a function of the form y = x â h The range is y â„ 0 .The graph of y = x â 4 is a horizontal translation (of 4 units to the right) of the graph of y = . x
3. EXAMPLE 5 Graph a function of the form y = a x â h + k Graph the function y = 2 â 1 . SOLUTION STEP 1 STEP 2 So, h = â4 and k = â1 . Shift the graph left 4 units and down 1 unit. x + 4 Sketch the graph of y = 2 . x y = 2 â 1 = 2 x â (â4) + (â1) . x + 4 Shift the graph h units horizontally and k units vertically. Notice that
4. GUIDED PRACTICE for Examples 4 and 5 5. Graph the function y = x + 3 and identify its domain and range. Compare the graph with the graph of y = x . Domain: x â„ â 3 ; Range: y â„ 0 ; Horizontal translation 3 units to the left ANSWER
5. GUIDED PRACTICE for Examples 4 and 5 6. Identify the domain and range of the function in Example 5 . The domain is x â„ â 4 . The range is y â„ â1 . ANSWER