By Fred Safier, Kimberly S. Kirkpatrick

Authoritative. Concise. Easy-to-Use. Schaum's effortless Outlines are streamlined types of best-selling Schaum's titles. we have shortened the textual content, broadened the appearance, and brought learn thoughts to make studying any topic more straightforward. the consequences are reader-friendly examine courses with the entire awesome educational authority of the originals. Schaum's effortless Outlines characteristic: Concise textual content that specializes in the necessities of the direction Quick-study sidebars, icons, and different tutorial aids pattern difficulties and workouts for overview

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**Example text**

A simple approach to finding a sketch of a graph is to find several solutions, plot them, then connect the dots with a smooth curve or line. 2: Sketch the graph of the equation x − 2y = 10. Form a table of values; then plot the points and connect them. The graph is a straight line, as shown in Figure 4-2. CHAPTER 4: Analytic Geometry and Functions 41 Figure 4-2 Intercepts The coordinates of the points where the graph of an equation crosses the x-axis and y-axis have special names: 1. The x-coordinate of a point where the graph crosses the x-axis is called the x-intercept of the graph.

42 PRECALCULUS Tests for symmetry: 1. If substituting −x for x leads to the same equation, the graph has symmetry with respect to the y-axis. 2. If substituting −y for y leads to the same equation, the graph has symmetry with respect to the x-axis. 3. If simultaneously substituting − x for x and − y for y leads to the same equation, the graph has symmetry with respect to the origin. Note: It is not possible for a graph to have exactly two of these three symmetries. It must have none, one, or all three symmetries.

The element y of E is called the image of x under f, or the value of f at x, and is written f(x). The subset R of E consisting of all images of elements of D is called the range of the function. The members of the domain D and range R are referred to as the input and output values, respectively. 6: Let D be the set of all words in English having fewer than 20 letters. Let f be the rule that assigns to each word the number of letters in the word. , the set of natural numbers less than 20). f assigns to the word “truth” the number 5; this would be written f(truth) = 5.