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Worksheet: Intersections of Exponential Functions with the Coordinate Axes

Q1:

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.

Q2:

What is the point of intersection of the 𝑦 -axis and the graph of the function 𝑓 ( π‘₯ ) = 9    ?

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

Q3:

What is the point of intersection of the 𝑦 -axis and the graph of the function 𝑓 ( π‘₯ ) = 9    ?

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

Q4:

For what values of π‘Ž is the function 𝑓 ( π‘₯ ) = π‘Ž π‘₯ increasing on its domain?

  • A π‘Ž = 1
  • B 0 < π‘Ž < 1
  • C π‘Ž > 0
  • D π‘Ž > 1

Q5:

Find the domain and range of 𝑓 ( π‘₯ ) = ο€Ό 1 8  π‘₯ , and determine whether it is an increasing function or a decreasing function.

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

Q6:

Determine whether the function is increasing or decreasing.

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

Q7:

Suppose that 𝑓 ( π‘₯ ) = 0 . 3 ( 4 ) π‘₯ .

Evaluate 𝑓 ( 0 ) .

Evaluate 𝑓 ( 2 ) .

Evaluate 𝑓 ( 0 . 5 ) .

Evaluate 𝑓 ο€Ό βˆ’ 1 2  .

Q8:

The curve with equation is the image of the curve with equation under reflection in which axis?

  • A -axis
  • B -axis

Q9:

The curve with equation is the image of the curve with equation under reflection in which axis?

  • A -axis
  • B -axis

Q10:

The graph shows the two functions 𝑓 ( 𝑑 ) = 1 0 ο€Ή 0 . 9 4   and 𝑔 ( 𝑑 ) = 1 5 ο€Ή 0 . 9 4   defined for 𝑑 β‰₯ 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 ( 𝑑 ) = 1 0 π‘Ž  and 𝑔 ( 𝑑 ) = 1 5 𝑏  with π‘Ž , 𝑏 > 0 . How do π‘Ž and 𝑏 compare if 𝑓 ( 𝑇 ) = 𝑔 ( 𝑇 ) at some point 𝑇 ?

  • A π‘Ž > 𝑏
  • B π‘Ž β‰  𝑏
  • C π‘Ž < 𝑏
  • D π‘Ž = 𝑏

Q11:

Find the domain and range of 𝑓 ( π‘₯ ) = 8 π‘₯ βˆ’ 2 , and determine whether it is an increasing function or a decreasing function.

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

Q12:

Find the point of intersection of the graph of 𝑓 ( π‘₯ ) = 2 π‘₯ 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 )

Q13:

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

  • A π‘Ž < 0
  • B π‘Ž > 0
  • C βˆ’ 1 < π‘Ž < 0
  • D 0 < π‘Ž < 1