EXAMPLE 1 Compare graph of y = with graph of y = a x 1 x 1 3x3x b. The graph of y = is a vertical shrink of the graph of. x y = 1 = y 1 x a. The graph.

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Presentation transcript:

EXAMPLE 1 Compare graph of y = with graph of y = a x 1 x 1 3x3x b. The graph of y = is a vertical shrink of the graph of. x y = 1 = y 1 x a. The graph of y = is a vertical stretch with a reflection in the x – axis of the graph of. –2 x

SOLUTION EXAMPLE 2 Graph y = + 3 and identify its domain and range. Compare the graph with the graph of y =. 1 x 1 x Graph the function using a table of values. The domain is all real numbers except 0. The range is all real numbers except 3. The graph of y = + 3 is a vertical translation (of 3 units up) of the graph of y =. 1 x 1 x Graph y = + k 1 x

EXAMPLE 2 xy –22.5 –12 – undefined Graph y = + k 1 x

SOLUTION EXAMPLE 3 Graph y = and identify its domain and range. Compare the graph with the graph of y =. 1 x – 2 1 x Graph the function using a table of values. The domain is all real numbers except 2. The range is all real numbers except 0. The graph of y = is a horizontal translation (of 2 units to the right) of the graph of y =. x– 2 1 x 1 Graph y = 1 x – h

EXAMPLE 3 xy 0– 0.5 1–1 1.5–2 2 undefined Graph y = 1 x – h

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 = 1 x ANSWER 1. y = – 4 x Domain: all real numbers except 0 Range: all real numbers except 0 The graph is a vertical stretch of y = that is then reflected in the x -axis. 1 x

GUIDED PRACTICE for Examples 1, 2 and 3 2. y = 1 x – 4 1 x Domain: all real numbers except 0 Range: all real numbers except – 4 The graph is a vertical translation (of 4 units down) of the graph y =. ANSWER Graph the function and identify its domain and range. Compare the graph with the graph of y = 1 x

GUIDED PRACTICE for Examples 1, 2 and 3 3. y = 1 x x Domain: all real numbers except – 5 Range: all real numbers except 0 The graph is a horizontal translation (of 5 units left) of the graph y =. Graph the function and identify its domain and range. Compare the graph with the graph of y = 1 x ANSWER

GUIDED PRACTICE for Examples 1, 2 and 3 y = 1 x Describe how the graph of is related to the graph of y =. 1 x The graph of y = is a horizontal translation (of 3 units left) of the graph of y =. x x 1 ANSWER