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Evaluating Exponential Functions (2)

In this worksheet, students substitute numerical values (including negative numbers and fractions) into exponential functions.

'Evaluating Exponential Functions (2)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Interpret Simple Expressions as Functions, Inverse Functions or Composite Functions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

An exponential function is one where the exponent or power is the variable, such as

f(x) = 4x 

In this function, we get:

f(0) = 40 = 1

f(1) = 41 = 4

f(2) = 42 = 16

f(3) = 43 = 64

f(-2) = 4-2 = 1/42 = 1/16

f(½) = 4½ = √4 = 2

f(1½) = 43/2 = (√4)3 = 23 = 8

 

Example

Use the following function to find f(1½)

f(x) = 3(16)x - 2

 

Answer

To find f(1½), we substitute 3/2 for x to get:

f(1½) = 3(16)3/2 - 2

 

163/2 is (161/2)3 = 43 = 64 so we get

 

f(1½) = 3 x 64 - 2 = 192 - 2 = 190

 

f(1½) = 190

Use the following function to find f(½)

 

f(x) = 4x

Use the following function to find f(½)

 

f(x) = 9x + 3

Use the following function to find f(-2)

 

f(x) = (2)x + 7

Use the following function to find f(-2)

 

f(x) = 2(4)x + 7

Use the following function to find f(-4)

 

f(x) = 5x + 1

Use the following function to find f(0)

 

f(x) = 88x + 49

Use the following function to find f(½)

 

f(x) = 7(25)x + 4

Use the following function to find f(3/2)

 

f(x) = 25x - 44

Use the following function to find f(-½)

 

f(x) = 16x + 44

Use the following function to find f(½)

 

f(x) = (¼)x - ½

  • Question 1

Use the following function to find f(½)

 

f(x) = 4x

CORRECT ANSWER
2
EDDIE SAYS
4½ = √4
  • Question 2

Use the following function to find f(½)

 

f(x) = 9x + 3

CORRECT ANSWER
6
EDDIE SAYS
9½ + 3 = √9 + 3
  • Question 3

Use the following function to find f(-2)

 

f(x) = (2)x + 7

CORRECT ANSWER
7.25
EDDIE SAYS
2-2 + 7 = 1 ÷ 4 + 7
  • Question 4

Use the following function to find f(-2)

 

f(x) = 2(4)x + 7

CORRECT ANSWER
7.125
EDDIE SAYS
2 × 4-2 + 7 = 2 × (1/16) + 7
  • Question 5

Use the following function to find f(-4)

 

f(x) = 5x + 1

CORRECT ANSWER
1.0016
EDDIE SAYS
5-4 + 1 = 1/625 + 1
  • Question 6

Use the following function to find f(0)

 

f(x) = 88x + 49

CORRECT ANSWER
50
EDDIE SAYS
880 + 49 = 1 + 49
  • Question 7

Use the following function to find f(½)

 

f(x) = 7(25)x + 4

CORRECT ANSWER
39
EDDIE SAYS
7 × 25½ + 4 = 7 × √25 + 4
  • Question 8

Use the following function to find f(3/2)

 

f(x) = 25x - 44

CORRECT ANSWER
81
EDDIE SAYS
253/2 - 44 = (√25)3 - 44 = 125 - 44
  • Question 9

Use the following function to find f(-½)

 

f(x) = 16x + 44

CORRECT ANSWER
44.25
EDDIE SAYS
16 + 44 = 1/√16 + 44
  • Question 10

Use the following function to find f(½)

 

f(x) = (¼)x - ½

CORRECT ANSWER
0
EDDIE SAYS
¼½ - ½ = √¼ - ½ = ½ - ½
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