Worksheet: Domain and Range of Exponential Functions

In this worksheet, we will practice identifying exponential functions, finding the domain and range described in their xy-plane graphs, and representing the equation graphically.

Q1:

The function 𝑓 ( 𝑥 ) = 𝑎 𝑥 is an exponential function if 𝑎 is any and 𝑥 is any .

  • A real number, real number
  • Breal number, positive real number except 1
  • C negative real number, real number
  • Dpositive real number except 1, real number

Q2:

Find the range of the function 𝑓 ( 𝑥 ) = 1 0 .

  • A ( , )
  • B ( , 0 )
  • C [ 0 , )
  • D ( 0 , )

Q3:

What is the domain of this exponential function?

  • A ( 0 , )
  • B ( 1 , )
  • C ( , 0 )
  • Dall real numbers
  • E ( 1 , )

Q4:

Which of the following is an exponential function?

  • A 𝑓 ( 𝑥 ) = ( 8 )
  • B 𝑓 ( 𝑥 ) = 2 𝑥
  • C 𝑓 ( 𝑥 ) = 1 𝑥 + 2
  • D 𝑓 ( 𝑥 ) = 2 1 7 ( 4 )

Q5:

Find the domain and the range of the function 𝑓 ( 𝑥 ) = 7 ( 9 ) .

  • A domain = , range =
  • B domain = , range =
  • C domain = , range =
  • D domain = , range =
  • E domain = , range = ( 7 , )

Q6:

Find the domain and the range of the function 𝑓 ( 𝑥 ) = 7 + 5 in .

  • A domain = ( 5 , ) , range =
  • B domain = , range =
  • C domain = , range =
  • D domain = , range = ( 5 , )
  • E domain = , range = ( 7 , )

Q7:

Given that 𝑎 > 1 , for which values of 𝑥 is 𝑎 > 1 𝑥 ?

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥 +

Q8:

Find the domain and the range of the function 𝑓 ( 𝑧 ) = 1 8 | | .

  • A domain = , range =
  • B domain = , range =
  • C domain = [ 0 , 1 ) , range =
  • D domain = , range = ( 0 , 1 ]
  • E domain = , range = ( 9 , )

Q9:

Determine the range of the function ( 𝑥 ) = 2 1 2 + 1 , giving your answer in interval notation.

  • A ( 0 , 2 )
  • B ( 1 , )
  • C ( 1 , 1 )
  • D ( 1 , 2 )
  • E ( 2 , 1 )

Q10:

The points on the graph show the population, in millions, of the Republic of Malawi for various years between 1960 and 2016. The population growth over these years can be modeled by the function 𝑃 ( 𝑥 ) = 3 . 6 2 ( 1 . 0 2 9 ) 𝑥 , which is also shown.

What is the domain of the function 𝑃 ?

  • A1960 𝑥 2016
  • Ball whole numbers
  • C 𝑥 0
  • D 0 𝑥 5 6
  • E 𝑥 < 0

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.