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Practice

5.14.5 Practice

5.14.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Functions a , b , c , d , e , and f are given below. Which functions are linear? Select the three answers that apply.
  1. a ( x ) = 3 x
  2. b ( x ) = 3 x
  3. c ( x ) = x 3
  4. d ( x ) = 9 + 3 x
  5. e ( x ) = 9 ⋅ 3 x
  6. f ( x ) = 9 ⋅ 3 x
  1. Functions a , b , c , d , e , and f are given below. Which functions are exponential? Select the two answers that apply.
  1. a ( x ) = 3 x
  2. b ( x ) = 3 x
  3. c ( x ) = x 3
  4. d ( x ) = 9 + 3 x
  5. e ( x ) = 9 ⋅ 3 x
  6. f ( x ) = 9 ⋅ 3 x
  1. Here are 4 equations defining 4 different functions, a , b , c , and d . List them in order of increasing rate of change. That is, start with the one that grows the slowest and end with the one that grows the quickest.
    • a ( x ) = 5 x + 3
    • b ( x ) = 3 x + 5
    • c ( x ) = x + 4
    • d ( x ) = 1 + 4 x
  1. Option 1: a ( x ) , b ( x ) , c ( x ) , d ( x )
  2. Option 2: d ( x ) , c ( x ) , b ( x ) , a ( x )
  3. Option 3: a ( x ) , d ( x ) , b ( x ) , a ( x )
  4. Option 4: c ( x ) , b ( x ) , d ( x ) , a ( x )

Use the given information for problems 4 – 6. Technology is required. Function f is defined by f ( x ) = 3 x + 5 , and function g is defined by g ( x ) = ( 1.1 ) x .

f ( x ) g ( x )
1
5
10
20

  1. Which values will complete the table for f ( x ) ?
  1. 8, 15, 30, 60
  2. 3, 15, 30, 60
  3. 8, 20, 35, 65
  4. 8, 11, 14, 17
  1. Which of the following sets of values will complete the table for g ( x ) ?
  1. 1.1, 1.21, 1.33, 1.46
  2. 1.1, 1.6, 2.59, 6.73
  3. 1.1, 5.5, 10.10, 20.20
  4. 8, 20, 35, 65

    1. ________ is a linear function.
  1. f ( x )
  2. g ( x )
  3. neither
    1. ________ is an exponential function.
  1. f ( x )
  2. g ( x )
  3. neither
  1. Functions m and n are given by m ( x ) = ( 1.05 ) x and n ( x ) = 5 8 x . As x increases from 0, __________ reaches 30 first.
  1. m ( x )
  2. n ( x )
  3. neither
  1. Functions m and n are given by m ( x ) = ( 1.05 ) x and n ( x ) = 5 8 x . As x increases from 0, __________ reaches 100 first.
  1. m ( x )
  2. n ( x )
  3. neither
  1. The functions f and g are defined by f ( x ) = 8 x + 33 and g ( x ) = 2 ⋅ ( 1.2 ) x . Which function eventually grows faster, f or g ? Explain how you know.
  1. g ( x ) grows faster because it is an exponential function.
  2. g ( x ) grows faster because it is a linear function.
  3. f ( x ) grows faster because 33 is greater than 2.
  4. f ( x ) grows faster because 8 is greater than 1.2.
  1. A line segment of length l is scaled by a factor of 1.5 to produce a segment with length m . The new segment is then scaled by a factor of 1.5 to give a segment of length n .

    What scale factor takes the segment of length l to the segment of length n ?