Help wanted:
NEL
Chapter
1
Introduction to
Functions
GOALS
You will be able to
• Identify a function as a special type
of relation
• Recognize functions in various
representations and use function notation
• Explore the properties of some basic
functions and apply transformations
to those functions
• Investigate the inverse of a linear function
and its properties
? Anton needs a summer job. How
would you help him compare the
two offers he has received?
NEL
1
1 Getting Started
SKILLS AND CONCEPTS You Need
1. Simplify each expression.
Study Aid 1 2 3
a) 3(x 1 y) 2 5(x 2 y) c) (x 1 1) 2 (x 2 2 1)
For help, see the Essential Skills 2 2
Appendix. b) (4x 2 y) (4x 1 y) d) 4x(x 1 2) 2 2x(x 2 4)
Question Appendix 2. Evaluate each expression in question 1 when x 5 3 and y 5 25.
1 A-8 3. Solve each linear equation.
5 3
2 A-7 a) 5x 2 8 5 7 c) y 2 y 5 23
6 4
4 A-5
x22 2x 1 1
5 A-15 b) 22(x 2 3) 5 2(1 2 2x) d) 5
4 3
6 A-12
4. Graph each linear relation.
7 A-14 a) y 5 2x 2 3 b) 3x 1 4y 5 12
8 A-9, A-10 5. Graph each circle.
a) x2 1 y2 5 9 b) 3x2 1 3y2 5 12
6. Graph each parabola, labelling the vertex and the axis of symmetry.
a) y 5 x2 2 6 c) y 5 23(x 1 4) 2 1 2
b) y 5 (x 2 2) 2 2 1 d) y 5 2x2 1 6x
7. For each quadratic relation, list the transformations you need to apply to
y 5 x2 to graph the relation. Then sketch the graph.
1
a) y 5 x2 2 2 c) y 5 (x 2 1) 2 2 4
2
b) y 5 24x2 1 3 d) y 5 22(x 1 3) 2 1 5
8. Solve each quadratic equation.
a) x 2 2 5x 1 6 5 0 b) 3x 2 2 5 5 70
9. Compare the properties of linear relations, circles, and quadratic relations.
Begin by completing a table like the one shown. Then list similarities and
differences among the three types of relations.
Property Linear Relations Circles Quadratic Relations
Equation(s)
Shape of graph
Number of quadrants
graph enters
Descriptive features
of graph
Types of problems
modelled by the
relation
2 Chapter 1 NEL
Getting Started
APPLYING What You Know
Fencing a Cornfield YOU WILL NEED
• graph paper
Rebecca has 600 m of fencing for her cornfield. The creek that goes through her
farmland will form one side of the rectangular boundary. Rebecca considers
different widths to maximize the area enclosed.
? How are the length and area of the field related to its width?
A. What are the minimum and maximum values of the width of the field?
B. What equations describe each?
i) the relationship between the length and width of the field
ii) the relationship between the area and width of the field
C. Copy and complete this table of values for widths that go from the least to
the greatest possible values in intervals of 50 m.
Width (m) Length (m) Area (m2)
D. Graph the data you wrote in the first two columns. Use width as the
independent variable. Describe the graph. What type of relationship is this?
E. Now graph the data you wrote in the first and third columns. Use width as
the independent variable again. Describe the graph. What type of
relationship is this?
F. How could you have used the table of values to determine the types of
relationships you reported in parts D and E?
G. How could you have used the equations from part B to determine the types
of relationships you reported in parts D and E?
NEL Introduction to Functions 3
