What You’ll Learn:
•Identifying families of functions for equations
and graphs.
•To predict what the graph of the equation
looks like.
What You’ll Need:
•Graphing calculator
•Note cards
Work with a partner.
1. Graph each equation using the standard range
setting. To help you keep track, sketch each graph
on a note card. Label it with the correct equation.
y = x2 – 6
y=x+2
y= x –4
||
y = |x – 3|
y = 7x
y = 3x2
y = x2 + 1
y = -3x
2. A. Sort the cards into three categories by
grouping graphs that look alike.
B. What similarities among the graphs in
each category do you see?
C. What similarities among the equations in
each category do you see?
The categories you made can help you make predictions.
3. What does the graph of y = 2x2 look like?
4. What can you say about the equation of this
graph?
You’ve already seen how grouping
functions that are alike can help
you make predictions. These
groups are called families of
functions. You can identify what
family a function belongs to by
looking at its equation.
To what family of functions does each
equation belong? Explain.
A. y = 2x – 6
Its highest power of x is 1.
So, y = 2x – 6 is a
linear function.
B.
y = -8x2
Its highest power of x is 2.
So, y = -8x2 is a
quadratic function.
5.The equation y = |x + 7| is an
absolute value function. What
characteristic of the equation tell
you this?
6. To what family of functions does each
equation belong?
EXPLAIN.
A.
y = 6x2 + 1
||
B.
y=3 x
C.
y = x2 + 3x + 2
7. Create three equations that belong to
the quadratic family of functions.
y=
–2
2
y = -x
2
4x
y=
2
2x
–x+1
You can identify what a family of function
belongs to by looking at its graph.
To what family of functions does each graph belong? Explain.
a.
b.
8. A. The equation y = -5x belongs to
what family of functions? How do
you know?
Linear; the highest
power of x is 1.
B. Look at the graph of y = -5x.
What characteristic of a graph
tells you it belongs to the linear
family of functions?
The graph is a straight line.
y=x+2
y = -x2 + 5
y = |x+2|
The highest power of x is 1.
The highest power of x is 2.
There is an absolute value symbol
around a variable expression..
To what family of functions does each equation belong?
Explain.
4
y  x7
1.
7
Quadratic function;
2
the
highest
power
of
x
is
2.
y


x
 11
2. _________________________
Linear function;
the highest power of x is 1.
_________________________
3.
Quadratic function;
the highest power of x is 2.
_________________________
y  0 .5 x
4.
Quadratic function;
the highest power of x is 2.
_________________________
y  49  x
2
2
To what family of functions does each equation belong?
Explain.
5.
Quadratic function;
the highest power of x is 2.
_________________________
Absolute value function;
There is a variable expression inside
the absolute value symbol.
6. _________________________
Absolute value function;
There is a variable expression inside
the absolute value symbol.
7. _________________________
8.
Linear function;
the highest power of x is 1.
_________________________
y  6 x  13 x  5
2
y  2 x
y  2  3x
1
y x
4
To what family of functions does each equation belong?
Explain your reasoning.
Absolute Value;
graph forms a
“v” that opens
up.
Absolute Value;
graph forms a
“v” that opens
down.
Quadratic;
graph is a Ushaped curve
that opens down.
12.The recommended dosage D in milligrams of a
certain medicine depends on a person’s body
weight w in kilograms. To what family of
functions does the formula D = 0.1w2 + 5n
belong? Explain.
Quadratic; the highest
power of x is 2.
13.Why are these graphs not
quadratic or absolute value
functions?
They fail the verticalline test.
14.Is a vertical line the graph of
a linear function? Why or
why not?
No; it fails the vertical-line
test so it is not a function.
15.Write two linear, two
quadratics, and two absolute
value equations.
Samples:
y=x+1
y = 3x + 6
y = x2 + x y = -3x2 + 9
y = x + 2  y = -x + 4  - 1
What characteristics do you look for to identify the
families of each?
Function
Graph of a quadratic
function
Equation of a linear
function
Graph of an absolute
value function
Equation of a quadratic
function
Characteristic
Determine to which family of functions each
graph belongs. Then sketch a model
each situation.
20. Income is a function of hours worked.
linear
21. Height of a fly ball is a function of time.
quadratic