Algebra: Form and Function
Format: PDF / Kindle (mobi) / ePub
This book offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. It relies on a storyline to form the backbone of the chapters and make the material more engaging. Conceptual exercise sets are included to show how the information is applied in the real world. Using symbolic notation as a framework, business professionals will come away with a vastly improved skill set.
Interpret Functions 85 Constants and Variables 86 Functions and Equivalent Expressions 87 4.3 Functions and Equations 89 Using Equations to Find Inputs from Outputs 89 Reading Solutions from the Graph 90 How Do We Know When Two Functions Are Equal? 91 Functions and Inequalities 92 4.4 Functions and Change 95 An Expression for the Average Rate of Change 96 Interpreting the Expression for Average Rate of Change 97 Using Units to Interpret the Average Rate of Change 98 4.5 Functions and Modeling
= f (Independent). Example 4 The cost in dollars of tuition, T , at most colleges is a function of the number of credits taken, c. Express the relationship in function notation and identify the independent and dependent variables. Solution We have Tuition cost = f (Number of credits), or T = f (c). The independent variable is c, and the dependent variable is T . Example 5 The area of a circle of radius r is given by A = πr2 . What is the independent variable? What is the dependent
miles from the subway. Which letters are constants and which are variables if (a) You want an apartment of 1000 square feet? (b) You want an apartment 1 mile from the subway? (c) You want an apartment that costs $200,000? 4.3 FUNCTIONS AND EQUATIONS Using Equations to Find Inputs from Outputs In the last section we saw how to evaluate an expression to find the output of a function given an input. Sometimes we want to find the inputs that give a certain output. To do that, we must solve an
the end of each hour into the trip. Assume each stops for gas just as the tank is empty, and then the tank is filled instantaneously. (b) Use your table to determine when they have the same amount of gas. (c) If they drive at the same speed while driving and only stop for gas, which of them gets to San Diego first? (Assume filling up takes time.) (d) Now suppose that between 1 hour and 6.5 hours outside of Tucson, all of the gas stations are closed unexpectedly. Does Antonio arrive in San Diego?
species consumes 60 calories per day on these activities, find a linear equation relating s and d and sketch its graph, placing d on the vertical axis. Say what the s- and dintercepts of the graph tell you about the bird. 161. A second species must consume 4 calories for each hour spent singing and 12 calories for each hour spent defending its territory. If this species also consumes 60 calories per day on these activities, find a linear equation relating s and d and sketch its graph, placing d