Transcript 3.7 Formulas and Functions

Algebra
3.7
Formulas and Functions
Formulas

A formula is an algebraic equation that relates two
or more real-life quantities

Formulas have more than one variable

Formulas are used in science, business, geometry and
everyday life.
rt = d
Distance Formula
p = 2l + 2w
Perimeter of a rectangle
A = ½bh
Area of a triangle
V = lwh
Volume of a rectangular prism
C = 5/9 (F-32)
Temperature conversion (F to C)
Solving a formula
When we solve a formula for an
indicated variable, you simply isolate
that variable on one side of the
equation.
To do this, you use inverse operations.
Solve the triangle area formula:
Solve for b
A = ½bh
A = ½bh
Ask yourself, where is the b
and what’s happening to it.
(2) A = ½bh (2)
The b is being multiplied by ½
and by h, so you want to
divide by½ (multiply by 2)…..
2A = bh
2A = bh
h
h
2A = b
h
and divide by h.
So, b = 2A
h
Solve the rectangle perimeter
formula: Solve for w
P = 2l + 2w
P = 2l + 2w
Ask yourself, where is the w
and what’s happening to it.
P
-2l
The w is being multiplied by 2
and that product is being
added to 2l, so first subtract
2l…..
= 2l + 2w
-2l
P – 2l = 2w
P – 2l = 2w
2
2
P – 2l = w
2
and then divide by 2.
So, w = P – 2l
2
Try these yourself!


Solve for h:
Answer:
V = l wh
h= V
lw
Solve for F:
C = 5 (F – 32)
9
Hint: First isolate (F – 32)
Answer:
F = 9 C + 32
5
Functions

A function is a rule that establishes a relationship
between two quantities, called the input and the
output

A linear function usually uses the variable x to
describe input, and y to describe output

A two-variable equation is written in function form if
the y is isolated on one side of the equation
Function form:
The output y
y = 2x + 4
is a function of the input x
Writing Function Form (you will
learn why you do this later)

When you write the equation in function form, arrange
the terms in the order below:
Function form:
Put the y
on the left
y = mx + b
Put the x term first
on the right
Put the
constant last
Write the fractions out as individual terms, such as
4 x and
5
1x
3
Rewrite the equation in Function
Form (isolate y)
2x + 3y = 10
2x + 3y = 10
Ask yourself, where is the y
and what’s happening to it.
2x + 3y = 10
-2x
-2x
The y is being multiplied by 3
and that product is being
added to 2x, so first
subtract 2x…..
3y = -2x + 10
3y = -2x + 10
3
3
y = - 2x + 10
3
3
and divide by 3.
So, y = - 2x + 10
3
3
Rewrite the equation in Function
Form (isolate y)
y - 7 = 7x - 9x
5
y - 7 = -2x
5
+7
+7
(5) y = (-2x + 7) (5)
5
y = -10x + 35
First, simplify the right side.
Next, add 7 to get the y
term alone
Then, multiply by 5. Make
sure that you multiply EVERY
TERM on BOTH SIDES by 5
So, y = - 10x + 35
Now you try these


Rewrite in function form:
x + 2y = 6
Answer:
y = -1/2x + 3
Rewrite in function form:
1 y + 3 = -5x
4
Answer:
y = -20x - 12
Homework
pg. 177 # 11-29,
34-39 (calculator OK on these)