Worksheet: Monomial Functions

In this worksheet, we will practice graphing and analyzing monomial functions.

Q1:

Consider the function 𝑓(𝑥)=110𝑥.

Which of the following shows the graph of 𝑓?

  • A
  • B
  • C
  • D

What is the 𝑦-intercept of the function?

What is the domain of 𝑓?

  • A ( , 0 ]
  • B [ 0 , )
  • C

What is the range of 𝑓?

  • A ( , 0 ]
  • B [ 0 , )
  • C

On what interval is the function increasing?

  • A
  • B ( 0 , )
  • C ( , 0 )

On what interval is the function decreasing?

  • A ( , 0 )
  • B
  • C ( 0 , )

What happens to the value of 𝑓(𝑥) as 𝑥?

  • A 𝑓 ( 𝑥 )
  • B 𝑓 ( 𝑥 )

What happens to the value of 𝑓(𝑥) as 𝑥?

  • A 𝑓 ( 𝑥 )
  • B 𝑓 ( 𝑥 )

Q2:

Consider the function 𝑓(𝑥)=1100𝑥.

Which of the following shows the graph of 𝑓?

  • A
  • B
  • C
  • D

What is the 𝑦-intercept of the function?

What is the domain of 𝑓?

  • A
  • B [ 0 , )
  • C ( , 0 ]

What is the range of 𝑓?

  • A
  • B ( , 0 ]
  • C [ 0 , )

On what interval is the function increasing?

  • AThere are no intervals on which the function is increasing.
  • B ( 0 , )
  • C

On what interval is the function decreasing?

  • AThere are no intervals on which the function is decreasing.
  • B ( , 0 )
  • C

What happens to the value of 𝑓(𝑥) as 𝑥?

  • A 𝑓 ( 𝑥 )
  • B 𝑓 ( 𝑥 )

What happens to the value of 𝑓(𝑥) as 𝑥?

  • A 𝑓 ( 𝑥 )
  • B 𝑓 ( 𝑥 )

Q3:

The figure shows the graph of 𝑓(𝑥)=𝑥.

Consider the behavior of the function 𝑔(𝑥)=(𝑥+2)+5.

State the domain and the range of 𝑔.

  • ADomain: (,2)(2,), range: (5,)
  • BDomain: (,5)(5,), range: (2,)
  • CDomain: (,5)(5,), range: (2,)
  • DDomain: (,2)(2,), range: (5,)
  • EDomain: (,2)(2,), range: (5,)

Find lim𝑔(𝑥).

Find lim𝑔(𝑥).

State where the function has a discontinuity.

  • A 𝑥 = 5
  • B 𝑥 = 2
  • C 𝑥 = 2
  • D 𝑥 = 5

State the intervals over which 𝑔 is increasing and decreasing.

  • AIncreasing over (,5), decreasing over (5,)
  • BIncreasing over (,2), decreasing over (2,)
  • CIncreasing over (,5), decreasing over (5,)
  • DIncreasing over (,2), decreasing over (2,)
  • EIncreasing over (2,), decreasing over (,2)

Q4:

Consider the function 𝑓(𝑥)=3𝑥.

State the domain and range of the function.

  • ADomain: [0,), range: (0,)
  • BDomain: (0,), range: [0,)
  • CDomain: (,), range: [0,)
  • DDomain: [0,), range: [0,)
  • EDomain: [0,), range: (,)

Evaluate lim𝑓(𝑥).

  • A0
  • B
  • C

State the interval over which the function is continuous.

  • A ( 0 , )
  • B ( , )
  • C ( , 0 )
  • D ( , 0 ]
  • E [ 0 , )

State the intervals over which the function is increasing and/or decreasing.

  • AIncreasing on [0,)
  • BIncreasing on (,)
  • CIncreasing on [0,), decreasing on (,0]
  • DIncreasing on (0,)
  • EDecreasing on [0,)

Q5:

Consider the function 𝑓(𝑥)=4𝑥.

State the domain and range of the function.

  • ADomain: (,), range: (0,)
  • BDomain: (,), range: [0,)
  • CDomain: (,0), range: [0,)
  • DDomain: (,0), range: (0,)
  • EDomain: (,), range: (,)

Find lim𝑓(𝑥).

  • A
  • B
  • C0

Find lim𝑓(𝑥).

  • A
  • B0
  • C

State the intervals over which the function is continuous.

  • A ( 0 , )
  • B ( , 0 )
  • C ( , 0 ]
  • D ( , )
  • E [ 0 , )

State the intervals over which the function is increasing and decreasing.

  • ADecreasing on (0,), increasing on (,0)
  • BDecreasing on (,0], increasing on [0,)
  • CDecreasing on [0,), increasing on (,0]
  • DDecreasing on (,0), increasing on (0,)

Q6:

Consider the function 𝑓(𝑥)=5𝑥.

State the domain and range of the function.

  • ADomain: (,), range: (0,)
  • BDomain: (0,), range: (,)
  • CDomain: (0,), range: (0,)
  • DDomain: [0,), range: (0,)
  • EDomain: (0,), range: [0,)

Evaluate lim𝑓(𝑥).

State the interval over which the function is continuous.

  • A ( , )
  • B ( , 0 )
  • C ( 0 , )
  • D [ 0 , )
  • E ( , 0 ]

State the intervals over which the function is increasing and/or decreasing.

  • AIncreasing on (0,)
  • BIncreasing on (,0), decreasing on (0,)
  • CDecreasing on (0,)
  • DDecreasing on (,0), increasing on (0,)
  • EDecreasing on (,0)

Q7:

Consider the function 𝑓(𝑥)=3𝑥.

State the domain and range of the function.

  • ADomain: (0,), range: (0,)
  • BDomain: (,0)(0,), range: (,0)(0,)
  • CDomain: (,0)(0,), range: (0,)
  • DDomain: (,0)(0,), range: [0,)
  • EDomain: (,0), range: (0,)

Find lim𝑓(𝑥).

Find lim𝑓(𝑥).

State where the function has a discontinuity.

  • A 𝑥 =
  • B 𝑥 = 0
  • C 𝑥 =

State the intervals over which the function is increasing and decreasing.

  • AIncreasing over (0,), decreasing over (,0)
  • BIncreasing over (,0), decreasing over (0,)
  • CIncreasing over (,0], decreasing over (0,)
  • DIncreasing over (,0) and (0,), never decreasing
  • EIncreasing over (,0), decreasing over [0,)

Q8:

Consider the function 𝑓(𝑥)=14𝑥.

State the domain and the range of the function.

  • ADomain: (,0)(0,), range: (0,)
  • BDomain: (,0), range: (0,)
  • CDomain: (,), range: (0,)
  • DDomain: (,0)(0,), range: (,0)
  • EDomain: (0,), range: (0,)

Find lim𝑓(𝑥).

  • A0
  • B
  • C1
  • D

Find lim𝑓(𝑥).

  • A
  • B1
  • C
  • D0

Is the function undefined at any values? If yes, state the values.

  • ANo
  • BYes, at 𝑥=0

State the intervals over which the function is increasing and decreasing.

  • AIncreasing over [0,), decreasing over (,0)
  • BIncreasing over (0,), decreasing over (,0)
  • CIncreasing over (,1), decreasing over (1,)
  • DIncreasing over (1,), decreasing over (,1) over
  • EIncreasing over (,0), decreasing over (0,)

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.