MCR3U1
EXPLORING PROPERTIES OF PARENT FUNCTIONS
U2L3
PART A ~ INTRODUCTION
Every function can be classified as a member of a family – a collection of
functions sharing common characteristics.
LINEAR
QUADRATIC
y=x
y = 5x
y = 3x – 4
y = ¼x + 5
y = x2
y = 3(x – 2)2 + 4
y = x2 + 5x + 6
y = (x – 3)(x + 4)
Different functions,
but same family!
PART B ~ DEFINITIONS
parent function:
the simplest, or base, function in a family
ex. f(x) = x, g(x) = x2, etc.
asymptote:
a line that the graph of a relation or function approaches
but never touches; it can be a vertical, horizontal, or oblique
axis of symmetry:
a line that divides a figure into 2 congruent parts
PART C ~ GRAPHING THE PARENT FUNCTIONS BY TABLE OF VALUES
Equation of Function
f(x) = x
f(x) =
x2
Table of Values
x
y
2
1
0
–1
–2
x
2
1
0
–1
–2
y
Sketch of Graph
y
x
y
x
MCR3U1
U2L3
f (x)  x
1
f (x) 
x
x
0
1
4
9
16
y
x
3
y
y
x
y
2
1
x
1
2
1
3
0
1
3
1
2
–1
–2
–3
f (x)  x
x
2
1
0
–1
–2
Y
y
x
MCR3U1
U2L3
PART D ~ SUMMARY
Equation
of Function
Name of
Function
Sketch of Graph
Special Features/
Symmetry
y
f(x) = x
x
y
f(x) = x2
x
y
f (x)  x
x
y
f (x) 
1
x
x
y
f (x)  x
x
Domain
{…}
Range
{…}
 passes through the
origin (0,0)
 slope is equal to 1
 divides the plane
in half diagonally
 graph lies in Q1 & Q3




parabola opens up
vertex at the origin
y has a minimum value
y–axis is axis of
symmetry
 graph lies in Q1 & Q2
 half parabola opens to
the right
 starts at the origin
 x and y have minimum
values
 graph lies in Q1
 hyperbolic in shape
 x– and y–axes are
asymptotes
 lines y = x and y = –x
are axes of symmetry
 graph lies in Q1 & Q3




graph opens up
vertex at the origin
y has a minimum value
y–axis is axis of
symmetry
 graph lies in Q1 & Q2
HOMEWORK: p.28 #1, 2, 3