Notes Over 2.3The Graph of a FunctionThe Graph of a FunctionFinding the Domain and Range of a Function. 1. Use the graph of the function f to find the domain of f.

,2 52. Find the value of f(-2),

and f(2).

2f 4

3. Find the range of the graph.

,4 4

2f 4

Notes Over 2.3Zeros of a FunctionZeros of a FunctionFinding Zeros of a Function. Find the zeros of each function.

055 .4 23 xxx

x 2x 1

5x 012 x

0 5 2x 1

0 1x 1x 5x5x 1x 1x

Notes Over 2.3Zeros of a FunctionZeros of a FunctionFinding Zeros of a Function. Find the zeros of each function.

0 15 .5 2 x215 x 0

2 2

2x15

15x

Notes Over 2.3Zeros of a FunctionZeros of a FunctionFinding Zeros of a Function. Find the zeros of each function.

04

417 .6

2

x

x

0471 x417 x

4

17x

Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDescribe the increasing and decreasing behavior.

The function is decreasing over

the entire real line.

.7

Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDescribe the increasing and decreasing behavior.

The function is decreasing on the interval , 1increasing on the interval ,1 0decreasing on the interval ,0 1increasing on the interval ,1

.8

Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDescribe the increasing and decreasing behavior.

The function is increasing on the interval ,4 1constant on the interval ,1 2

decreasing on the interval ,2 5

.9

Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDetermining Relative Maximum or Minimum.

Relative Maximum

Relative Minimum

Notes Over 2.3Increasing and Decreasing FunctionsIncreasing and Decreasing FunctionsDetermining Relative Maximum or Minimum. 10.Use a graphing calculator to find the relative

maximum of the function:

11102 2 xxy

5.1 ,5.2

Notes Over 2.3Linear FunctionsLinear Functions11. Write the linear function f for which 14 f

5

1

2

31 m

10 64

and 36 f

y1y

11 xxmyy

x5

1

1 45

1

5

4 x

5

1

5

9

Notes Over 2.3Graphing a Piecewise FunctionGraphing a Piecewise Function

Graph the function.

2 if ,92

2 if ,42

1 .12

xx

xxxf

Notes Over 2.3Even and Odd FunctionsEven and Odd FunctionsDetermine if the function is even, odd, or neither.

24 2 .13 xxxf even isfunction then the, If xfxf odd isfunction then the, If xfxf

24 2 xf x x

24 2xxxf

Even function

Notes Over 2.3Even and Odd FunctionsEven and Odd FunctionsDetermine if the function is even, odd, or neither.

xxxf 45 .14 3 even isfunction then the, If xfxf odd isfunction then the, If xfxf

4 5 3 xf x x

xxxf 45 3 Odd function

Notes Over 2.3