Formulas and Functions Formulas are algebraic equations that relate two or more real-life quantities. They are standardized relationships that exist, which can be used to solve relational problems between variables given one. We can also manipulate the formulas to determine missing components given the total solution. Area Formulas: Area formulas relate length and width of an object, in a fixed relationship and ratio, in order to determine the area of the object. - Works with all variations, e.g. Area for a triangle: ½ bh Temperature Conversions: Relating temperature in Celsius to Fahrenheit and visa versa. - Who might use the first formula? - The second? A = lw l = A / w C = 5/9(f - 32) F = 9/5C + 32 * Can also be written as: F = 1.8C + 32

Interest Formulas: Using the standard formula for interest we can relate the various components of Principle, Rate, and Time, by transforming the standard formula. I = Prt r = I / Pt P = I / rt t = I / Pr Example: Find the interest rate for an investment of $1500 that earned $54 in simple interest in one year. What if you were given the $54 and the rate for one year, could you determine the original investment amount (p)?

d = rt t = d / r r = d / t Distance Formula: Distance = Rate x Time. Time = Distance divided by Rate. Rate = Distance divided by Time Mars Pathfinder: Since it’s landing on July 4, 1997 the Mars Pathfinder has returned over 2.6 billion bits of information including more than 16,550 images of Mars. The Pathfinder was launched on December 4, 1996. During its 212 day flight to Mars it traveled about 310million miles. Estimate the time (in days) it would have taken to reach Mars at the following speeds. 30,000 mph 40,000 mph 60,000 mph 80,000 mph Which is the best estimate of the Pathfinder’s average speed on it’s journey to Mars?

Rewriting Equations in Function Form Equations can be converted into functions by rewriting the equation in terms of setting the format as y = some function of x. The isolated variable is then the output side of the function, which is a direct function of the inputs for the other variable. Example: 3x + y = 4 -3x = - 3x Subtract 3x from both sides y = 4 – 3x This equation now represents y as a function of x We can also re-write the equation to state x as a function of y. - y = - y Subtract y from each side 3x = 4 – y 3 3 Divide each side by 3 x = 4 – y 3

Evaluating the Function for values of x and y Given the newly created functions, we can evaluate each equation for a variety of values for x and y. The inputs and outputs of each function can also be stated in a table or column format. y = 4 – 3x x = 4 – y 3 Input (x) Output (y) Input (y) Output (x) 0 4 0 4/3 1 1 1 1 2 -2 2 2/3 -1 7 -1 5/3 -2 10 -2 2