5.8 Review

  1. Plot each point on the coordinate planes provided. Label each point with the assigned letter. If possible, identify the quadrant in which the points are located. Identify the domain and range for each graph. Determine whether each graph is a function.

    a)
    Blank coordinate plane. Both axes have a minimum of -8 and maximum of 8 and a scale of 2.a (–4, 1)
    b (–2, 3)
    c (2, –5)
    d (–2, 5)
    e (–3, \frac{5}{2})    		 b)
    Blank coordinate plane. Both axes have a minimum of -8 and maximum of 8 and a scale of 2.a (0, 0)
    b (0, –3)
    c (–4, 0)
    d (1, 0)
    e (0, –2)

  2. Complete the table of values for the equations.

    a) y=-4x+1

    x y (x, y)
    –1
    –3
    3
    5
    b) 2x-5y=10
    x y (x, y)
    –5
    0
    5
    2

  3. Graph the following equations.

    a) y=-4x
    Blank coordinate plane. Both axes have a minimum of -12 and maximum of 12 and a scale of 2.    		 b) 2x+y=-3
    Blank coordinate plane. Both axes have a minimum of -8 and maximum of 8 and a scale of 2.

  4. Identify the x-intercept(s) and y-intercept(s) of the graphs below. Identify the domain and range for each graph. Determine whether each graph is a function.

    a)
    The graph of the equation y = −x + 2. The x-intercept is the point (2, 0) and the y-intercept is the point (0, 2).    		 b)
    Graph of the equation y = − 1 half x + 2. The x-intercept is the point (4, 0) and the y-intercept is the point (0, 2).

  5. Algebraically determine the intercepts of the following equations.

    a) x+4y=8

     

     

     

    		 b) 2x-4y=8

     

     

     
    c) x-y=5

     

     

     

    		 d) 3x-2y=12

     

     

     
    e) y=\frac{1}{3}x+1

     

     

     

    		 f) y=3x

     

     

     

  6. Identify the domain and range for each graph.

    a)
    Sideways parabola opening right with vertex at (-1,2).    		 b)
    Horizontal line passing through y=-2.

  7. Which of the following real-life situations does not represent a function?

    a) The amount of water in a tank as a function of time.
    b) The colour of a car as a function of the car model.
    c) The price of a ticket as a function of the time you purchase it.
    d) The number of cars on the road at a particular moment in time.

  8. Determine which of the following relations are functions. Explain why or why not.

    a) (2, 3), (4, –5), (1, –5), (6, 0), (−3, 8)
    		 b) (5, 4), (−2, 5), (5, −6), (1, 7), (5, 5)
    c)
    Half of the parabola y=x^2 where x>0. Note vertex is at (0,0)
    		 d)
    Circle graph x spans -2 to 2 and y spans -2 to 2.

  9. Consider the function: f(x)=3-6x. Round to the nearest tenth where necessary.

    a) Evaluate for f(-2) .

     

     

     

    		 b) Solve for f(x)=9.

     

     

     

    		 c) Evaluate for f(2x+3).

     

     

     
    d) Evaluate f(3)+f(5).

     

     

     

    		 e) Solve for f(x)=-20.

     

     

     

    		 f) Evaluate f(-1)-f(6).

     

     

     
  10. Vita went to a museum, but it wasn’t open. She decided to buy a museum ticket online to go the next day. When she went to the museum’s website, she noticed that if she got a membership and bought more than one ticket to the museum, admission would be cheaper. To become a member, there was a flat fee of $5, then it would cost $5 for each visit. The equation T=5n+5 can be used to represent the relationship between the number of admissions Vita decides to purchase, n, and the total cost, T.
    a) Fill in the table of values.
    b) Label each axis and give the graph a title.
    c) Plot the points, then draw a line to connect the points.
    Number of Admissions Total Cost ($) (x, y)
    0
    5
    10
    15
    20
    Quadrant 1 of a blank coordinate plane. The x-axis has a minimum of 0 and maximum of 50 and a scale of 1. The y-axis has a minimum of 0 and maximum of 260 and a scale of 5.

    d) What is the T-intercept of this graph? What does it represent?

    e) What is the n-intercept of this graph? What does it represent?

    f) Vita decides she is going to have her birthday party at the museum. If she is going to get tickets for herself and 15 friends, how much will it cost her?

     

     

    g) Vita ends up spending $110. How many tickets did she purchase?

     

     

    h) If you cannot have more than 50 tickets on your membership at a time, what are the real-life domain and range?

     

     

    i) Is the equation that represents this situation a function? Why or why not?

Answers

1.

a)
A graph plotting the points described in the previous paragraph.		 b)
A graph plotting the points a (0, 0), b (0, negative 3), c (negative 4, 0), d (1, 0), e (0, negative 2).
a III, b II, c IV, d II, e II

Domain = {–4, –2, 2, –3}
Range = {1, 3, –5, 5, \frac{5}{2}}

It is not a function.

 A point on an axis is not considered to be in a quadrant, so none of these points is in a quadrant.

Domain = {0, –4, 1}
Range = {0, –3, –2}

It is not a function.
2.

a)

x y (x, y)
–1 5 (–1, 5)
1 –3 (1, –3)
3 –11 (3, –11)
5 –19 (5, –19)
b)
x y (x, y)
–5 –4 (–5, –4)
0 –2 (0, –2)
5 0 (5, 0)
10 2 (10, 2)
3.

a)
Graph of the equation y = -4x.		 b)
Graph of the equation 2x + y = −3.
4.

a) (2, 0), (0, 2)
Domain = {x\in\mathbb{R}}
Range = {y\in\mathbb{R}}
It is a function.		 b) (4, 0), (0, 2)
Domain = {x\in\mathbb{R}}
Range = {y\in\mathbb{R}}
It is a function.
5.

a) (8, 0), (0, 2) b) (4, 0), (0, –2) c) (5, 0), (0, –5)
d) (4, 0), (0, –6) e) (–3, 0), (0, 1) f) (0, 0), (0, 0)
6.

a) Domain = {x\leq -1,x\in\mathbb{R}}
Range = {y\in\mathbb{R}}		 b) Domain = {x\in\mathbb{R}}
Range = {y=-2}

7. b

8.

a) function b) not a function c) function d) not a function
9.

a) 15 b) –1 c) -12x-15 d) –42 e) 3.8 f) 42
10.

a)

Number of Admissions Total Cost ($) (x, y)
0 5 (0, 5)
5 30 (5, 30)
10 55 (10, 55)
15 80 (15, 75)
20 105 (20, 105)

d) T-int = 5. If Vita does not buy any tickets, she will have to pay $5 for the membership.
e) n-int = –1. Vita cannot buy –1 tickets, so this point is not relevant to this graph.
f) $85
g) 21 tickets
h) Domain = {0\leq n\leq 50,n\in\mathbb{R}}
Range = {0\leq T\leq 255,T\in\mathbb{R}}
i) It is a function because there is a maximum of one output for each input.

 b) and c)
Graph of T=5n+5

Attribution

Unless otherwise indicated, material on this page has been adapted from the following resource:

Mazur, I. (2021). Introductory algebra. BCcampus. https://collection.bccampus.ca/textbooks/intermediate-algebra-bccampus-412/, licensed under CC BY 4.0

 

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Math 10C Workbook Copyright © 2026 by Leanne Thompson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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