3.7 Formulas and Functions
Algebra 1
3.7 FORMULAS AND FUNCTIONS
Solving Formulas
So far we have been solving equations with one variable. However, many of the equations we will be using
throughout the course have more than one variable. You have used equations that have multiple variables in your
science and math classes every time you use a formula. Formulas for Area, Perimeter, Circumference, Distance,
Celsius to Fahrenheit, Interest, etc. have appeared in math and science classes in the recent past. Sometimes it is
useful to rewrite these formulas in order to create a “new” formula.
Knowing how to rewrite formulas means you only need to remember ONE version because you can always solve for
the other “version” of the formula. For instance, in science classes you have been given two different formulas to
convert between temperature scales. If you know how to rewrite the formula, then you only need to remember one.
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( F − 32 ) . Find the formula to
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convert Celsius to Fahrenheit by solving the equation above for F instead of C, and use your “new” formula to
convert 55° C to Fahrenheit.
Example: The formula to convert Fahrenheit to Celsius is given by C =
Example: In chapter one, we used the formula d = rt . Find a formula for t in terms of d and r.
Example: Using the formula for perimeter of a rectangle, solve for w. P = 2l + 2w
Example: Not everything has to be a known formula. Solve the following equation for x: ax + b = c
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3.7 Formulas and Functions
Algebra 1
Rewriting Equations in Function Form
A two – variable equation is written in function form if one of its variables is isolated on one side of the equation.
The isolated variable (also known as the variable you solve for) is the output and is a function of the input.
Example: In the equation V = 4π r 2 . The output is _____________. The input is ______________. We say
One of the more important concepts in Algebra is functions. Being able to rewrite an equation in function form will
help simplify this process. Graphing calculators (even though you cannot use them right now) are useless for
graphing unless YOU know how to rewrite the equation in function form. Most of these calculators actually have a
button on them the looks like o.
Throughout the year, we will need to write equations so that they begin “y =”. This only involves solving the
equation for y. When we do this we can say that y is a function of x.
Example: Rewrite the equation so that y is a function of x. The first one is worked out for you.
(a) 6x – 2y = 8
–2y = 8 – 6x
y = –4 + 3x
What was done to both sides?
What was done to both sides?
(b) 3x + y = 7
(c) 2 x − 3 y = 9
Example: Using the results from parts (b) and (c), make an input-output table when the domain is {–5, –2, 0, 1, 3}.
(a)
(b)
Input
Input
Output
Example: On another sheet of paper, rewrite the equation so that y is a function of x.
Bring me your answer!
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Output
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( 25 − 5 y ) = 4 x − 9 y + 13
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