Lesson Worksheet: Exponential Functions Mathematics • 9th Grade

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In this worksheet, we will practice identifying, writing, evaluating, and analyzing exponential functions.

Q1:

What are the base and exponent of the function 𝑓(𝑥)=5?

  • Abase =𝑥−5, exponent =5
  • Bbase =5, exponent =𝑥−5
  • Cbase =5, exponent =𝑥+5
  • Dbase =𝑥+5, exponent =5

Q2:

Write an exponential equation in the form 𝑦=𝑎(𝑏) for the numbers in the table.

𝑥0123
𝑦186223
  • A𝑦=2(3)
  • B𝑦=1813
  • C𝑦=3(2)
  • D𝑦=13(18)
  • E𝑦=2𝑥

Q3:

Given that 𝑓(𝑥)=6, determine the value of 𝑓(3).

  • A1216
  • B18
  • C216
  • D118
  • E−216

Q4:

Suppose that 𝑓(𝑥)=0.3(4).

Evaluate 𝑓(0).

Evaluate 𝑓(2).

Evaluate 𝑓(0.5).

Evaluate 𝑓−12.

Q5:

Write an exponential equation in the form 𝑦=𝑏 for the numbers in the table.

𝑥245
𝑦916812562431,024
  • A𝑦=34
  • B𝑦=916
  • C𝑦=932
  • D𝑦=(𝑥)
  • E𝑦=(𝑥)

Q6:

Given that 𝑓(𝑥)=3, find 𝑓(𝑥+9).

  • A3
  • B3
  • C3
  • D3

Q7:

Consider an exponential function with base 𝑎. For which values of 𝑎 is the function decreasing?

  • A𝑎>0
  • B0<𝑎<1
  • C𝑎<0
  • D−1<𝑎<0

Q8:

Observe the given graph, and then answer the following questions.

Find the 𝑦-intercept in the shown graph.

As this graph represents an exponential function, every 𝑦-value is multiplied by 𝑏 when 𝑥 increases by Δ𝑥. Find 𝑏 for Δ𝑥=1.

Find the equation that describes the graph in the form 𝑦=𝑎𝑏.

  • A𝑦=10⋅2
  • B𝑦=2
  • C𝑦=10⋅14
  • D𝑦=10⋅12
  • E𝑦=10⋅4

Q9:

Given that 𝑓(𝑥)=8 and 𝑓(𝑥)=18, determine the value of 𝑓−𝑓(−4)𝑓−𝑓(−2).

Q10:

Given that 𝑓(𝑥)=4, determine the value of 𝑓(𝑥)𝑓(𝑥−1)−𝑓(𝑥−1)𝑓(𝑥).

  • A154
  • B415
  • C174
  • D417

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