Warm-up
1. Graph y = 3x.
ANSWER
2. Tell whether the ordered pairs (0, 0), (1, 2), (2, 4),
and (3, 6) represent a linear function.
3. For y = x2 – 3x – 5, find corresponding y-values for
the x-values –2, 1, and 3.
10.8 Compare Linear, Exponential,
and Quadratic Models
•Students will Compare Linear, Exponential,
and Quadratic Models
Identifying from an equation:
Linear
Quadratic
Exponential
Has an x with
no exponent.
Has an x2 in the
equation.
Has an x as
the exponent.
y = 5x + 1
y = ½x
2x + 3y = 6
y = 2x2 + 3x – 5
y = x2 + 9
x2 + 4y = 7
y = 3x + 1
y = 52x
4x + y = 13
Examples:
• LINEAR, QUADRATIC or EXPONENTIAL?
a)y = 6x + 3
b)y = 7x2 +5x – 2
c)9x + 3 = y
d)42x = 8
Identifying from a graph:
Linear
Quadratic
Exponential
Makes a
straight line
Makes a U or ∩
Rises or falls
quickly in one
direction
LINEAR, QUADRATIC or EXPONENTIAL?
a)
b)
c)
d)
Is the table linear, quadratic or
exponential?
Linear
• Never see the
same y value
twice.
• 1st difference
is the same
Quadratic
• See same y
more than
once.
• 2nd difference
is the same
Exponential
• y changes
more quickly
than x.
• Never see the
same y value
twice.
• Common
multiplication
pattern
EXAMPLE 2
b.
Identify functions using differences or ratios
x
–2
–1
0
1
2
y
–2
1
4
7
10
Differences:
3
3
3
3
ANSWER
The table of values represents a linear function.
EXAMPLE 2
Identify functions using differences or ratios
Use differences or ratios to tell whether the table of
values represents a linear function, an exponential
function, or a quadratic function.
a.
x
y
–2
–6
First differences: 0
Second differences: 2
–1
–6
0
–4
2
1
0
4
2
2
6
6
2
ANSWER
The table of values represents a quadratic function
.
GUIDED PRACTICE
2.
for Examples 1 and 2
Tell whether the table of values represents a
linear function, an exponential function, or a
quadratic function.
ANSWER
x
–2
–1
0
1
y
0.08
0.4
2
10
exponential function
x
y
x
y
0
-5
-2
-2
1
-4
-1
-4
2
-1
0
-8
3
4
2
-32
4
11
5
-256
Is the table linear, quadratic or
exponential?
x
y
x
y
x
y
1
5
1
0
1
3
2
9
2
-1
2
9
3
13
3
0
3
27
4
17
4
3
4
81
5
21
5
8
5
243
EXAMPLE 3
Write an equation for a function
Tell whether the table of values represents a linear
function, an exponential function, or a quadratic
function. Then write an equation for the function.
x
–2
–1
0
1
2
y
2
0.5
0
0.5
2
EXAMPLE 3
Write an equation for a function
SOLUTION
STEP 1 Determine which type of function the table of
values represents.
x
–2
–1
0
1
2
y
2
0.5
0
0.5
2
First differences: –1.5
Second differences: 1
–0.5
0.5
1
1.5
1