Inverse Functions
Learning Objectives In this section, you will: A reversible heat pump is a climate-control system that is an air conditioner and a heater in a single device. Operated in one direction, it pumps heat out of a house to provide…
Absolute Value Functions
Learning Objectives In this section, you will: Figure 1 Distances in deep space can be measured in all directions. As such, it is useful to consider distance in terms of absolute values. (credit: “s58y”/Flickr) Until the 1920s, the so-called spiral nebulae were…
Transformation of Functions
Learning Objectives In this section, you will: Figure 1 (credit: “Misko”/Flickr) We all know that a flat mirror enables us to see an accurate image of ourselves and whatever is behind us. When we tilt the mirror, the images we see may…
Composition of Functions
Learning Objectives In this section, you will: Suppose we want to calculate how much it costs to heat a house on a particular day of the year. The cost to heat a house will depend on the average daily temperature,…
Rates of Change and Behavior of Graphs
Learning Objectives In this section, you will: Gasoline costs have experienced some wild fluctuations over the last several decades. Table 1 lists the average cost, in dollars, of a gallon of gasoline for the years 2005–2012. The cost of gasoline can be…
Domain and Range
Learning Objectives In this section, you will: Horror and thriller movies are both popular and, very often, extremely profitable. When big-budget actors, shooting locations, and special effects are included, however, studios count on even more viewership to be successful. Consider…
Functions and Function Notation
Learning Objectives In this section, you will: Horror and thriller movies are both popular and, very often, extremely profitable. When big-budget actors, shooting locations, and special effects are included, however, studios count on even more viewership to be successful. Consider…
Introduction to Functions
Standard and Poor’s Index with dividends reinvested (credit “bull”: modification of work by Prayitno Hadinata; credit “graph”: modification of work by MeasuringWorth) Chapter Outline 3.1 Functions and Function Notation 3.2 Domain and Range 3.3 Rates of Change and Behavior of Graphs 3.4 Composition of…
Linear Inequalities and Absolute Value Inequalities
Learning Objectives In this section, you will: Figure 1 It is not easy to make the honor roll at most top universities. Suppose students were required to carry a course load of at least 12 credit hours and maintain a grade…
Other Types of Equations
Learning Objectives In this section, you will: We have solved linear equations, rational equations, and quadratic equations using several methods. However, there are many other types of equations, and we will investigate a few more types in this section. We…