Algebra I

4.7Graph Linear Functions

EXAMPLE 1

f (x) 3x – 15=

= (– 3) 3(– 3) – 15f

ANSWER

The correct answer is A. A B C D

= 24

GUIDED PRACTICE

1. Evaluate the function h(x) = – 7x when x = 7.

h(7) = – 49

=f(x) 6.2. For the function f(x) 2x – 10, find the value of x so that=

= 2x – 10f(x)

6 2x – 10=

8 x=

The gray wolf population in central Idaho was monitored over several years for a project aimed at boosting the number of wolves.

The number of wolves can be modeled by the function

f(x) = 37x + 7

where x is the number of years since 1995.

Graph the function and identify its domain and range.

GRAY WOLF

EXAMPLE 3

EXAMPLE 3

To graph the function, make a table.

x f(x)

0 37(0) + 7 = 7

1 37(1) + 7 = 44

2 37(2) + 7 = 81

The domain of the function is x 0. From the graph or table, you can see that the range of the function is f(x) 7.

>=

>=

Graph a function

2. WOLF POPULATION Use the model from Example 3 to find the value of x so that f(x) = 155. Explain what the solution means in this situation.

SOLUTION

x f(x)

0 37(0) + 7 = 7

1 37(1) + 7 = 442 37(2) + 7 = 813 37(3) + 7 = 118

4 37(4) + 7 = 155

4 years after 1995, the wolf population will be 155.

EXAMPLE 4

Graph the function. Compare the graph with the graph of f (x) x.=

a. g(x) = x + 3

Because the graphs of g and f have the same slope, m = 1, the lines are parallel. Also, the y- intercept of the graph of g is 3 more than the y-intercept of the graph of f.

h(x) = 2xb.

Because the slope of the graph of h is greater than the slope of the graph of f, the graph of h rises faster from left to right. The y-intercept for both graphs is 0, so both lines pass through the origin.

GUIDED PRACTICE

Graph h(x) = – 3x. Compare the graph with the graph of f (x) = x.

3.

Since the slope of the graph of h is negative the graph of h falls from left to right.

The y-intercept for both graphs is 0, so both lines pass through the origin.

EXAMPLE 5 CABLE

A cable company charges new customers $40 for installation and $60 per month for its service.

The cost to the customer is given by the function f(x) = 60x +40 where x is the number of months of service.

To attract new customers, the cable company reduces the installation fee to $5.

A function for the cost with the reduced installation fee is g(x) = 60x + 5. Graph both functions. How is the graph of g related to the graph of f ?

EXAMPLE 5

The graphs of both functions are shown.

Both functions have a slope of 60, so they are parallel.

The y-intercept of the graph of g is 35 less than the graph of f.

So, the graph of g is a vertical translation of the graph of f.