Formulas & Functions

Formula – an algebraic expression that relates two or more real-life quantities

Solving a Temperature Conversion Formula

Solve the temperature formula C= (F - 32) for F95

SolutionC= (F - 32) Write the original Formula

C= (F - 32) Multiply each side by 9/5

C= F - 32 Simplify

C + 32 = F - 32 + 32 Add 32 to each side

C + 32 = F Simplify

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Rewriting Equations in Function Form

• The isolated variable is the output and is a function of the input

• Example

P = 4s This formula describes the perimeter P of a square as a function of it’s side length s

Rewriting an equation in function formRewrite the equation y + 3 = -5x so that y is a

function of x.

y + 3 – 3 = -5x – 3 Subtract 3 from both sides

y = -5x – 3 Simplify

4 y = (-5x – 3) 4 Multiply both sides by 4

y = -20x – 12 Simplify

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Rewrite the equation 2y + 5 = -4x + 7 so that y is a function of x.Then use the result to find y when x = 1, 2, 0, -2

• 2y + 5 = -4x + 7 Rewrite the equation• -5 -5 Subtract 5 from both sides• 2y = (-4x + 2) Simplify• /2 /2 Divide both sides by 2• y = -2x + 1 Simplify

x y = -2x + 1 y1 y = -2(1) + 1 -1

2 y = -2(2 ) + 1 -3

0 y = -2(0) +1 1

-2 y = -2(-2 ) +1 5