Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 1a – Introduction to Functions Mini-Lesson Problem 2 WORKED EXAMPLE – INVESTIGATING FUNCTIONAL RELATIONSHIPS Let’s investigate the functional relationship between the two quantities, “numerical grade” and “letter grade”. First, let Numerical Grade be the input quantity and Letter Grade be the output quantity. Below is a sample data set that is representative of the situation. Numerical grade Letter Grade 95 A 92 A 85 B 73 C The numbers above are made up to work with this situation. Other numbers could be used. We are assuming a standard 90, 80, 70, etc… grading scale. Hopefully you can see from this data that no matter what numerical value we have for input, there is only one resulting letter grade. Notice that the repeated outputs “A” are not a problem since the inputs are different. You can uniquely predict the output for any numerical grade input. So, from this information we can say that Letter Grade (output) is a function of Numerical Grade (input). Now let’s switch the data set above. Letter Grade Numerical Grade A 95 A 92 B 85 C 73 Can you see there is a problem here? If you say that you have an A in a class, can you predict your numerical grade uniquely? No. There are a whole host of numerical scores that could come from having an A. The same is true for all the other letter grades as well. Therefore, Numerical Grade (output) is NOT a function of Letter Grade (input). Summary: Letter Grade IS a function of Numerical Grade but Numerical Grade is NOT a function of Letter Grade Additional Terminology In the language of functions, the phrase INDEPENDENT VARIABLE means input and the phrase DEPENDENT VARIABLE means output. The dependent variable (output) “depends on” or is a “function of” the independent variable (input). Scottsdale Community College Page 4 Intermediate Algebra
Lesson 1a – Introduction to Functions Mini-Lesson Problem 3 MEDIA EXAMPLE – DO THE DATA REPRESENT A FUNCTION? The table below gives the height, in feet, of a golf ball t seconds after being hit. t = Time (in seconds) H = Height (in feet) 0 0 1 80 2 128 3 144 4 128 5 80 6 0 a) Identify the input quantity (include units)._________________________________________ Identify the input variable._________________________________________________ Identify the output quantity (include units).________________________________________ Identify the output variable._________________________________________________ b) Write the data as a set of ordered pairs. c) Interpret the meaning of the ordered pair (3, 144). d) Is height of the golf ball a function of time? Why or why not? e) Is time a function of the height of the golf ball? Why or why not? Problem 4 MEDIA EXAMPLE – DOES THE STATEMENT DESCRIBE A FUNCTION? Explain your choice for each of the following. Remember when the word “function” is used, it is in a purely MATHEMATICAL sense, not in an everyday sense. a) Is the number of children a person has a function of their income? b) Is your weekly pay a function of the number of hours you work each week? (Assume you work at an hourly rate job with no tips). Scottsdale Community College Page 5 Intermediate Algebra
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Intermediate Algebra – Student Workbook – Second Edition 2013

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