Lesson 4: Using Function Notation to Describe Rules (Part 1)

Using Function Notation to Describe Rules (Part 1)

Student Summary

Some functions are defined by rules that specify how to compute the output from the input. These rules can be verbal descriptions or expressions and equations. For example:

Rules in words:

Rules in function notation:

To get the output of function $f$ , add 2 to the input, then multiply the result by 5.

$f(x) = (x + 2) \boldcdot 5$ or $f(x)=5(x+2)$

To get the output of function $m$ , multiply the input by $\frac12$ and subtract the result from 3.

$m(x) = 3 - \frac12x$

Some functions are defined by rules that relate two quantities in a situation. These functions can also be expressed algebraically with function notation.

Suppose function $c$ gives the cost of buying $n$ pounds of apples at $1.49 per pound. We can write the rule $c(n) = 1.49n$ to define function $c$ .

To see how the cost changes when $n$ changes, we can create a table of values.

pounds of apples, $n$	cost in dollars, $c(n)$
0	0
1	1.49
2	2.98
3	4.47
$n$	$1.49n$

Plotting the pairs of values in the table gives us a graphical representation of $c$ .

<p>Points plotted. Horizontal axis, 0 to 8, n, pounds of apples. Vertical axis, 0 to 10, cost in dollars. Points at 0 comma 0, approximately 1 comma 1 point 5, 2 comma 3, 3 comma 4 point 5, 4 comma 6.</p>

Visual / Anchor Chart

Standards

Building On

8.F.1

8.F.A.1

Addressing

F-IF.2

HSF-IF.A.2

F-IF.1

HSF-IF.A.1

F-BF.1.a

F-IF.2

F-IF.4

F-IF.C

HSF-BF.A.1.a

HSF-IF.A.2

HSF-IF.B.4

HSF-IF.C

Building Toward

F-BF.1

HSF-BF.A.1