Lesson Worksheet: Exponential Functions Mathematics • 9th Grade

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

Q1:

What are the base and exponent of the function ๐‘“(๐‘ฅ)=5๏—๏Šฑ๏Šซ?

  • Abase =๐‘ฅโˆ’5, exponent =5
  • Bbase =5, exponent =๐‘ฅโˆ’5
  • Cbase =5, exponent =๐‘ฅ+5
  • Dbase =๐‘ฅ+5, exponent =5

Q2:

Write an exponential equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆ186223
  • A๐‘ฆ=2(3)๏—
  • B๐‘ฆ=18๏€ผ13๏ˆ๏—
  • C๐‘ฆ=3(2)๏—
  • D๐‘ฆ=13(18)๏—
  • E๐‘ฆ=2๐‘ฅ๏Šฉ

Q3:

Given that ๐‘“(๐‘ฅ)=6๏—, determine the value of ๐‘“(3).

  • A1216
  • B18
  • C216
  • D118
  • Eโˆ’216

Q4:

Suppose that ๐‘“(๐‘ฅ)=0.3(4)๏—.

Evaluate ๐‘“(0).

Evaluate ๐‘“(2).

Evaluate ๐‘“(0.5).

Evaluate ๐‘“๏€ผโˆ’12๏ˆ.

Q5:

Write an exponential equation in the form ๐‘ฆ=๐‘๏— for the numbers in the table.

๐‘ฅ245
๐‘ฆ916812562431,024
  • A๐‘ฆ=๏€ผ34๏ˆ๏—
  • B๐‘ฆ=๏€ผ916๏ˆ๏—
  • C๐‘ฆ=๏€ผ932๏ˆ๏—
  • D๐‘ฆ=(๐‘ฅ)๏Žจ๏Ž ๏Žฅ
  • E๐‘ฆ=(๐‘ฅ)๏Žข๏Žฃ

Q6:

Given that ๐‘“(๐‘ฅ)=3๏—๏Šฑ๏Šฎ, find ๐‘“(๐‘ฅ+9).

  • A3๏—๏Šฐ๏Šง๏Šญ
  • B3๏Šจ๏—๏Šฐ๏Šง
  • C3๏—๏Šฐ๏Šง
  • D3๏Šจ๏—๏Šฐ๏Šง๏Šญ

Q7:

Consider an exponential function with base ๐‘Ž. For which values of ๐‘Ž is the function decreasing?

  • A๐‘Ž>0
  • B0<๐‘Ž<1
  • C๐‘Ž<0
  • Dโˆ’1<๐‘Ž<0

Q8:

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

Find the ๐‘ฆ-intercept in the shown graph.

As this graph represents an exponential function, every ๐‘ฆ-value is multiplied by ๐‘ when ๐‘ฅ increases by ฮ”๐‘ฅ. Find ๐‘ for ฮ”๐‘ฅ=1.

Find the equation that describes the graph in the form ๐‘ฆ=๐‘Ž๐‘๏‘๏ซ๏‘.

  • A๐‘ฆ=10โ‹…2๏—
  • B๐‘ฆ=2๏—
  • C๐‘ฆ=10โ‹…๏€ผ14๏ˆ๏—
  • D๐‘ฆ=10โ‹…๏€ผ12๏ˆ๏—
  • E๐‘ฆ=10โ‹…4๏—

Q9:

Given that ๐‘“(๐‘ฅ)=8๏Šง๏— and ๐‘“(๐‘ฅ)=๏€ผ18๏ˆ๏Šจ๏—, determine the value of ๐‘“๏€ป๏‡โˆ’๐‘“(โˆ’4)๐‘“๏€ป๏‡โˆ’๐‘“(โˆ’2)๏Šง๏Šฏ๏Šจ๏Šจ๏Šง๏Šซ๏Šจ๏Šจ.

Q10:

Given that ๐‘“(๐‘ฅ)=4๏—, determine the value of ๐‘“(๐‘ฅ)๐‘“(๐‘ฅโˆ’1)โˆ’๐‘“(๐‘ฅโˆ’1)๐‘“(๐‘ฅ).

  • A154
  • B415
  • C174
  • D417

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