Holt Algebra 1

5-1 Identifying Linear Functions

Give the domain and range of each relation.

–4

–1

01

2

6

5

xy

x y

1 1

4 4

8 1 : /1 5D x x : / 3 4R y y

: 1, 2,5,6D x : 4, 1,0R y

: 1, 4,8D x : 1, 4R y

Holt Algebra 1

5-1 Identifying Linear Functions

Identify linear functions and linear equations.

Graph linear functions that represent real-world situations and give their domain and range.

Objectives

Holt Algebra 1

5-1 Identifying Linear Functions

The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight line. A function whose graph forms a straight line is called a linear function.

Holt Algebra 1

5-1 Identifying Linear Functions

Identify whether the graph represents a function. If the graph does represent a function, is the function linear?

The graph is a because every input

has one and only one outpu

function

linear funct

t. The graph is a

because it forms a straight ion line.

Holt Algebra 1

5-1 Identifying Linear Functions

Identify whether the graph represents a function. If the graph does represent a function, is the function linear?

The graph is a because every input

has one and only one output. The graph is not

a linear function because it does not form a

straigh

function

t line.

Holt Algebra 1

5-1 Identifying Linear Functions

Identify whether the graph represents a function. If the graph does represent a function, is the function linear?

The graph is not a function. 1 0 2 It's Linear!x y

Holt Algebra 1

5-1 Identifying Linear Functions

Identify whether the graph represents a function. If the graph does represent a function, is the function linear?

The graph is a because every input

has one and only one outpu

function

linear funct

t. The graph is a

because it forms a straight ion line.

Holt Algebra 1

5-1 Identifying Linear Functions

Identify whether the graph represents a function. If the graph does represent a function, is the function linear?

The graph is a because every input

has one and only one outpu

function

linear funct

t. The graph is a

because it forms a straight ion line.

Holt Algebra 1

5-1 Identifying Linear Functions

Identify whether the graph represents a function. If the graph does represent a function, is the function linear?

The graph is not a function.

Holt Algebra 1

5-1 Identifying Linear Functions

In a linear function, a constant change in x corresponds to a constant change in y.

Holt Algebra 1

5-1 Identifying Linear Functions

Tell whether the set of ordered pairs satisfies a linear function. Explain.

{(0, –3), (4, 0), (8, 3), (12, 6), (16, 9)}

4

3

the set satisf lineies a .ar function

x

y

In a linear function, a constant change in x corresponds to a constant change in y.

Holt Algebra 1

5-1 Identifying Linear Functions

{(–4, 13), (–2, 1), (0, –3), (2, 1), (4, 13)}

Tell whether the set of ordered pairs satisfies a linear function. Explain.

2

the relation is not a linear function.

x

y DNE

Holt Algebra 1

5-1 Identifying Linear Functions

Tell whether the set of ordered pairs {(3, 5), (5, 4), (7, 3), (9, 2), (11, 1)} satisfies a linear function. Explain.

2

1

the set satisf linear functionies a .

x

y

Holt Algebra 1

5-1 Identifying Linear Functions

Another way to determine whether a function is linear is to look at its equation. A function is linear if it is described by a linear equation. A linear equation is any equation that can be written in the standard form shown below.

1 0 2 It's Linear!x y

Holt Algebra 1

5-1 Identifying Linear Functions

Notice that when a linear equation is written in standard form

• x and y both have exponents of 1.• x and y are not multiplied together.• x and y do not appear in denominators, exponents, or radical signs.

For any two points, there is exactly one line that contains them both. This means you need only two ordered pairs to graph a line.

Holt Algebra 1

5-1 Identifying Linear Functions

Tell whether the function is linear. If so, graph the function.

x = 2y + 42y2y

2 4x y

the function lin is .ear

y

xyx04

20

Holt Algebra 1

5-1 Identifying Linear Functions

Tell whether the function is linear. If so, graph the function.

xy = 4

Notice that when a linear equation is written in standard form

• x and y both have exponents of 1.• x and y are not multiplied together.• x and y do not appear in denominators, exponents, or radical signs.

the function i ls not .inear

Holt Algebra 1

5-1 Identifying Linear FunctionsTell whether the function is linear. If so, graph the function.

y = 5x – 9

5x5x5 9x y

the function lin is .ear

y

xyx0

9 / 590

Holt Algebra 1

5-1 Identifying Linear FunctionsTell whether the function is linear. If so, graph the function.

y = 12 0 12x y

the function

l is .inear

y

x

Holt Algebra 1

5-1 Identifying Linear Functions

Tell whether the function is linear. If so, graph the function.

y = 2x

Notice that when a linear equation is written in standard form

• x and y both have exponents of 1.• x and y are not multiplied together.• x and y do not appear in denominators, exponents, or radical signs.

the function i ls not .inear

Holt Algebra 1

5-1 Identifying Linear Functions

For linear functions whose graphs are not horizontal, the domain and range are all real numbers. However, in many real-world situations, the domain and range must be restricted. For example, some quantities cannot be negative, such as time.

Holt Algebra 1

5-1 Identifying Linear Functions

Sometimes domain and range are restricted even further to a set of points. For example, a quantity such as number of people can only be whole numbers. When this happens, the graph is not actually connected because every point on the line is not a solution.

Holt Algebra 1

5-1 Identifying Linear Functions

The relationship between human years and dog years is given by the function y = 7x, where x is the number of human years. Graph this function and give its domain and range.

HW pp. 300-302/15-25 odd, 30-54 even, 57-72 

y

x1 2 3 4 5 6 7 8

714212835424956

yx04

028

: / 0D x x : / 0R y y