Function Rules, Tables and Graphs

Course 3

Section 5-3

Investigation: Functions

• Copy and Complete the table for squares

• Write answers on the hand out.

Make a graph of side length l and perimeter for order pairs (l,p)

Make a graph of side length l and area A for ordered pairs (l,A)

For which of the two graphs could you join the points to form a line?

Write two rules, one for finding the perimeter of a square with side length l and one for finding the area A of a square.

Three views of a function

• A Function can be written or viewed in 3 different ways

• 1) the function rule (Algebra)

• 2) Table of Values (inputs & outputs)

• 3) Graph (Visual, line/curve)

Example 1

• Model the function rule

• y = 1/2 x + 3 using a table of values and a graph

• Step 1 : Chose input values for x. Evaluate to find y. Choose two positive, two negative values and zero.

• Step 2: Plot points for the ordered pairs

• Step 3: Join the points to form a line.

• Model the rule f(x) = 3x + 4

Real-world situations

When you draw a graph for a real-world situation, choose appropriate intervals for the units on the axis. Be sure the intervals are equal. Also, if the data are positive numbers use only the first quadrant.

Example 2: Recording CostsSuppose your group recorded a new CD. Now

you want to copy and sell it. One company charges $250 for making a master CD and designing the art for the cover. There is also a cost of $3 to burn each CD. The total cost P(c) depends on the number of CDs burned. Use the function rule

P(c)=250+ 3c to make a table of values and a graph.

Rec

ordi

ng C

osts

(d

olla

rs)

Number of CDs

Second Company

• Another company charges $300 for making a master and designing the art. It charges $2.50 for buring each CD. Use the function rule P(c) = 300 + 2.5c. Make a table of values and graph.

Rec

ordi

ng C

osts

(d

olla

rs)

Number of CDs

Critical Thinking

• Compare your graph from Example 2 to the graph of the Second Company. For what number of CDs is the studio in Example 2 less expensive?

Graphing Functions

• Some functions have graphs that are not straight lines. You can graph a function as long as you know its rule. After you have graphs the ordered pairs that you have calculated from a rule, join points with a smooth line or curve.

Additional Examples

• Graph the function y = | x | + 1

• Graph the function f(x) = x2 + 1

• Make a table of values and graph each function• f(x) = | x | -1

• Graph the function y = x2 -1