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EXAMPLE 3

Begin by sketching the graph of y = , which passes through (0, 3) and . Then translate the graph left 1 unit and down 2 units .Notice that the translated graph passes through (– 1, 1) and. Graph y = 3 –2. State the domain and range. x – h.

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EXAMPLE 3

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  1. Begin by sketching the graph of y = , which passes through (0, 3) and . Then translate the graph left 1 unit and down 2 units .Notice that the translated graph passes through (– 1, 1) and Graph y = 3 –2. State the domain and range. x – h 1 – 1 1 3 Graph y = ab + k for 0 < b < 1 2 2 2 2 x 3 0, x+1 1, EXAMPLE 3 SOLUTION

  2. x – h Graph y = ab + k for 0 < b < 1 EXAMPLE 3 The graph’s asymptote is the line y = –2. The domain is all real numbers, and the range is y > –2.

  3. Snowmobiles A new snowmobile costs $4200. The value of the snowmobile decreases by 10% each year. EXAMPLE 4 Solve a multi-step problem • Write an exponential decay model giving the snowmobile’s value y (in dollars) after t years. Estimate the value after 3 years. • Graph the model. • Use the graph to estimate when the value of the snowmobile will be $2500.

  4. t y = a(1 –r) t = 4200(1 –0.10) t = 4200(0.90) When t = 3, the snowmobile’s value is y = 4200(0.90)3 = $3061.80. EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 The initial amount is a= 4200 and the percent decrease is r = 0.10. So, the exponential decay model is: Write exponential decay model. Substitute 4200 for aand 0.10 for r. Simplify.

  5. EXAMPLE 4 Solve a multi-step problem STEP 2 The graph passes through the points (0, 4200) and (1, 3780).It has the t-axis as an asymptote. Plot a few other points. Then draw a smooth curve through the points. STEP 3 Using the graph, you can estimate that the value of the snowmobile will be $2500 after about 5 years.

  6. x–1 4.y = +1 1 4 for Examples 3 and 4 GUIDED PRACTICE Graph the function. State the domain and range.

  7. x+1 2 5. y = 5 –2 3 for Examples 3 and 4 GUIDED PRACTICE Graph the function. State the domain and range.

  8. 3 4 x – 5 6. g(x) = –3 +4 for Examples 3 and 4 GUIDED PRACTICE Graph the function. State the domain and range.

  9. SOLUTION y = 4200(0.8)tAfter about 2 yr. for Examples 3 and 4 GUIDED PRACTICE 7.WHAT IF?In Example 4, suppose the value of the snowmobile decreases by 20% each year. Write and graph an equation to model this situation. Use the graph to estimate when the value of the snowmobile will be $2500.

  10. SOLUTION $3729.69 for Examples 3 and 4 GUIDED PRACTICE 8. SNOWMOBILE The value of a snowmobile has been decreasing by 7% each year since it was new. After 3 years, the value is $3000. Find the original cost of the snowmobile.

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