Warm-up

1. Graph y = 3x.

ANSWER

Tell whether the ordered pairs (0, 0), (1, 2), (2, 4), and (3, 6) represent a linear function.

2.

For y = x2 – 3x – 5, find corresponding y-values for the x-values –2, 1, and 3.

3.

10.8 Compare Linear, Exponential, and Quadratic Models

•Students will Compare Linear, Exponential, and Quadratic Models

Identifying from an equation:

Linear

Has an x with no exponent.

y = 5x + 1

y = ½x

2x + 3y = 6

Quadratic

Has an x2 in the equation.

y = 2x2 + 3x – 5

y = x2 + 9

x2 + 4y = 7

Exponential

Has an x as the

exponent.

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

Makes a straight line

Quadratic

Makes a U or ∩

Exponential

Rises or falls quickly in

one direction

LINEAR, QUADRATIC or EXPONENTIAL?

a) b)

c) d)

Is the table linear, quadratic or exponential?

Quadratic

• See same y more than once.

• 2nd difference is the same

Linear

• Never see the same y value twice.

• 1st difference is the same

Exponential

• y changes more quickly than x.

• Never see the same y value twice.

• Common multiplication pattern

Identify functions using differences or ratiosEXAMPLE 2

ANSWER

The table of values represents a linear function.

x – 2 – 1 0 1 2

y – 2 1 4 7 10

Differences: 3 3 3 3

b.

Identify functions using differences or ratios

EXAMPLE 2

Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function.

ANSWER

The table of values represents a quadratic function.

x –2 –1 0 1 2

y –6 –6 –4 0 6

First differences: 0 2 4 6

Second differences: 2 2 2

a.

GUIDED PRACTICE for Examples 1 and 2

2. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function.

ANSWER exponential function

0

y 2

x – 2 – 1 1

0.08 0.4 10

x y

0 -5

1 -4

2 -1

3 4

4 11

x y

-2 -2

-1 -4

0 -8

2 -32

5 -256

Is the table linear, quadratic or exponential?

x y1 0

2 -1

3 0

4 3

5 8

x y1 5

2 9

3 13

4 17

5 21

x y1 3

2 9

3 27

4 81

5 243

Write an equation for a functionEXAMPLE 3

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

SOLUTION

Write an equation for a functionEXAMPLE 3

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 –0.5 0.5 1.5

Second differences: 1 1 1