Worksheet: Intersections of Exponential Functions with the Coordinate Axes

In this worksheet, we will practice finding the intersection of an exponential function with the coordinate axes.

Q1:

What is the point of intersection of the 𝑦 -axis and the graph of the function 𝑓 ( 𝑥 ) = 9 ?

  • A ( 9 , 1 )
  • B ( 9 , 0 )
  • C ( 1 , 9 )
  • D ( 0 , 9 )

Q2:

The population of a country was 22 million people at the end of 2010. Since then, the population has increased by 1 . 8 % yearly. Determine the population of the country at the end of 2023. Give your answer in units of millions, correct to two decimal places.

Q3:

The curve with equation 𝑦 = 4 is the image of the curve with equation 𝑦 = 1 4 under reflection in which axis?

  • A 𝑦 -axis
  • B 𝑥 -axis

Q4:

Determine whether the function 𝑓 ( 𝑥 ) = 1 4 + 4 1 1 is increasing or decreasing.

  • Adecreasing on its range
  • Bdecreasing on its domain
  • Cincreasing on its range
  • Dincreasing on its domain

Q5:

Find the domain and range of 𝑓 ( 𝑥 ) = 1 8 , and determine whether it is an increasing function or a decreasing function.

  • Adomain = { 0 } , range = , decreasing on its domain
  • Bdomain = , range = , increasing on its domain
  • Cdomain = { 0 } , range = , increasing on its domain
  • Ddomain = , range = , decreasing on its domain

Q6:

Find the domain and range of 𝑓 ( 𝑥 ) = 8 , and determine whether it is an increasing function or a decreasing function.

  • Adomain = { 0 } , range = , increasing on its domain
  • Bdomain = , range = , decreasing on its domain
  • Cdomain = { 0 } , range = , decreasing on its domain
  • Ddomain = , range = , increasing on its domain

Q7:

For what values of 𝑎 is the function 𝑓 ( 𝑥 ) = 𝑎 𝑥 increasing on its domain?

  • A 𝑎 = 1
  • B 0 < 𝑎 < 1
  • C 𝑎 > 0
  • D 𝑎 > 1

Q8:

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

  • A 𝑎 < 0
  • B 𝑎 > 0
  • C 1 < 𝑎 < 0
  • D 0 < 𝑎 < 1

Q9:

The graph shows the two functions 𝑓 ( 𝑡 ) = 1 0 0 . 9 4 and 𝑔 ( 𝑡 ) = 1 5 0 . 9 4 defined for 𝑡 0 . Both are decaying at a rate of 6 % .

What is the ratio of 𝑔 ( 1 2 ) 𝑓 ( 1 2 ) ?

What is the ratio of 𝑔 ( 4 2 ) 𝑓 ( 4 2 ) ?

Suppose that 𝑓 ( 𝑡 ) = 1 0 𝑎 and 𝑔 ( 𝑡 ) = 1 5 𝑏 with 𝑎 , 𝑏 > 0 . How do 𝑎 and 𝑏 compare if 𝑓 ( 𝑇 ) = 𝑔 ( 𝑇 ) at some point 𝑇 ?

  • A 𝑎 > 𝑏
  • B 𝑎 𝑏
  • C 𝑎 < 𝑏
  • D 𝑎 = 𝑏

Q10:

Suppose that 𝑓 ( 𝑥 ) = 0 . 3 ( 4 ) .

Evaluate 𝑓 ( 0 ) .

Evaluate 𝑓 ( 2 ) .

Evaluate 𝑓 ( 0 . 5 ) .

Evaluate 𝑓 1 2 .

Q11:

Find the point of intersection of the graph of 𝑓 ( 𝑥 ) = 2 with the straight line 𝑦 = 1 6 .

  • A ( 1 6 , 2 )
  • B ( 1 6 , 4 )
  • C ( 2 , 1 6 )
  • D ( 4 , 1 6 )
  • E ( 2 , 4 )

Q12:

What is the point of intersection of the 𝑦 -axis and the graph of the function 𝑓 ( 𝑥 ) = 9 ?

  • A ( 9 , 2 )
  • B ( 8 1 , 0 )
  • C ( 2 , 9 )
  • D ( 0 , 8 1 )

Q13:

The curve with equation 𝑦 = 9 is the image of the curve with equation 𝑦 = 1 9 under reflection in which axis?

  • A 𝑦 -axis
  • B 𝑥 -axis

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