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EXAMPLE 7

log. a. . y. x. =. 3. EXAMPLE 7. Graph logarithmic functions. Graph the function. SOLUTION. Plot several convenient points, such as (1, 0) , (3, 1) , and (9, 2) . The y -axis is a vertical asymptote.

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EXAMPLE 7

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  1. log a. y x = 3 EXAMPLE 7 Graph logarithmic functions Graph the function. SOLUTION Plot several convenient points, such as (1, 0), (3, 1), and (9, 2). The y-axis is a vertical asymptote. From left to right, draw a curve that starts just to the right of the y-axis and moves up through the plotted points, as shown below.

  2. log b. y x = 1/2 EXAMPLE 7 Graph logarithmic functions Graph the function. SOLUTION Plot several convenient points, such as (1, 0), (2, –1), (4, –2), and (8, –3). The y-axis is a vertical asymptote. From left to right, draw a curve that starts just to the right of the y-axis and moves down through the plotted points, as shown below.

  3. Graph . State the domain and range. y (x + 3) + 1 = log log 2 2 Sketch the graph of the parent function y = x, which passes through (1, 0), (2, 1), and (4, 2). EXAMPLE 8 Translate a logarithmic graph SOLUTION STEP 1 STEP 2 Translate the parent graph left 3 units and up 1 unit. The translated graph passes through (–2, 1), (–1, 2), and (1, 3). The graph’s asymptote is x = –3. The domain is x > –3, and the range is all real numbers.

  4. log 16. y x = 5 for Examples 7 and 8 GUIDED PRACTICE Graph the function. State the domain and range. SOLUTION The domain is x > 0, and the range is all real numbers.

  5. log 17. y (x – 3) = 1/3 for Examples 7 and 8 GUIDED PRACTICE Graph the function. State the domain and range. SOLUTION domain: x > 3, range: all real numbers

  6. log 18. y (x + 1) – 2 = 4 for Examples 7 and 8 GUIDED PRACTICE Graph the function. State the domain and range. SOLUTION domain: x > –1, range: all real numbers

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