Holt Algebra 1

4-4 Graphing FunctionsSolve the inequality and graph the solutions.

45 + 2b > 614545

2 16b 228b

8 – 3y ≥ 2988

3 21y 337y

8

7

Holt Algebra 1

4-4 Graphing Functions

Graph functions given a limited domain.Graph functions given a domain of all real numbers.

Objectives

Holt Algebra 1

4-4 Graphing Functions

22 2 3 1f

Graph the function for the given domain.f(x) = x2 – 3; D: {–2, –1, 0, 1, 2}

y

x

21 1 3 2f

20 0 3 3f

21 1 3 2f 22 2 3 1f

Holt Algebra 1

4-4 Graphing FunctionsGraph the function for the given domain.–2x + y = 3; D: {–5, –3, 1, 4}

y

x

2 3 2 3y x f x x

5 2 5 3 7f

1 2 1 3 5f 4 2 4 3 11f

3 2 3 3 3f

Holt Algebra 1

4-4 Graphing Functions

If the domain of a function is all real numbers, any number can be used as an input value. This process will produce an infinite number of ordered pairs that satisfy the function. Therefore, arrowheads are drawn at both “ends” of a smooth line or curve to represent the infinite number of ordered pairs. If a domain is not given, assume that the domain is all real numbers.

Holt Algebra 1

4-4 Graphing Functions Graph the function –3x + 2 = y.

y

x

3 2y x

Holt Algebra 1

4-4 Graphing FunctionsGraph the function g(x) = |x| + 2.

y

x

x g x

2

0

2

42

4

Holt Algebra 1

4-4 Graphing FunctionsGraph the function f(x) = 3x – 2.

y

x

Holt Algebra 1

4-4 Graphing FunctionsGraph the function y = |x – 1|.

y

x

x y

2

0

1

3

2

1

1

2

0

1

Holt Algebra 1

4-4 Graphing FunctionsUse a graph of the function to find the value of f(x) when x = –4. Check your answer.

y

x

4,6

14 4 4 62

f

CHECK

Holt Algebra 1

4-4 Graphing FunctionsUse the graph of to find the value of x when f(x) = 3. Check your answer.

y

x

3,3

13 3 2 33

f

CHECK

Holt Algebra 1

4-4 Graphing Functions

Recall that in real-world situations you may have to limit the domain to make answers reasonable. For example, quantities such as time, distance, and number of people can be represented using only nonnegative values. When both the domain and the range are limited to nonnegative values, the function is graphed only in Quadrant I.

Holt Algebra 1

4-4 Graphing FunctionsA mouse can run 3.5 meters per second. The function y = 3.5x describes the distance in meters the mouse can run in x seconds. Graph the function. Use the graph to estimate how many meters a mouse can run in 2.5 seconds.

y

x 73.52

y x y x 1 2 3 4 5 6 7 8

48

121620242832

3.5 8 28 9 m

HW pp. 256-258/13-61 odd,64-71