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Worksheet: Domain and Range of Exponential Functions

Q1:

Find the range of the function 𝑓 ( π‘₯ ) = 1 0 π‘₯ .

  • A ( βˆ’ ∞ , ∞ )
  • B ( βˆ’ ∞ , 0 )
  • C [ 0 , ∞ )
  • D ( 0 , ∞ )

Q2:

What is the domain of this exponential function?

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

Q3:

The function 𝑓 ( π‘₯ ) = π‘Ž π‘₯ is an exponential function if π‘Ž is any and π‘₯ 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

Q4:

Find the domain and the range of the function .

  • A domain , range
  • B domain , range
  • C domain , range
  • D domain , range
  • E domain , range

Q5:

Find the domain and the range of the function in .

  • A domain = , range =
  • B domain = , range =
  • C domain = , range =
  • D domain = , range =
  • E domain = , range =

Q6:

Find the domain and the range of the function .

  • A domain , range
  • B domain , range
  • C domain , range
  • D domain , range
  • E domain , range

Q7:

Which of the following is an exponential function?

  • A 𝑓 ( π‘₯ ) = ( βˆ’ 8 ) π‘₯
  • B 𝑓 ( π‘₯ ) = 2 π‘₯ 2
  • C 𝑓 ( π‘₯ ) = 1 π‘₯ + 2
  • D 𝑓 ( π‘₯ ) = 2 1 7 ( 4 ) π‘₯

Q8:

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 ( π‘₯ ) = 3 . 6 2 ( 1 . 0 2 9 ) π‘₯ , which is also shown.

What is the domain of the function 𝑃 ?

  • A1960 ≀ π‘₯ ≀ 2016
  • Ball whole numbers
  • C π‘₯ β‰₯ 0
  • D 0 ≀ π‘₯ ≀ 5 6
  • E π‘₯ < 0

Q9:

Given that π‘Ž > 1 , for which values of π‘₯ is π‘Ž > 1 π‘₯ ?

  • A π‘₯ ∈ ℝ
  • B π‘₯ ∈ ℝ βˆ’
  • C π‘₯ ∈ β„€
  • D π‘₯ ∈ ℝ +

Q10:

Determine the range of the function β„Ž ( π‘₯ ) = 2 βˆ’ 1 2 + 1     , giving your answer in interval notation.

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