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Stitz-Zeager_College_Algebra_e-book

# To actually prove this analytically we assume x y is a

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Unformatted text preview: the axes hold special signiﬁcance. These are called the intercepts of the graph. Intercepts come in two distinct varieties: x-intercepts and y -intercepts. They are deﬁned below. Definition 1.3. Suppose the graph of an equation is given. • A point at which a graph meets the x-axis is called an x-intercept of the graph. • A point at which a graph meets the y -axis is called an y -intercept of the graph. In our previous example the graph had two x-intercepts, (−1, 0) and (1, 0), and one y -intercept, (0, 1). The graph of an equation can have any number of intercepts, including none at all! Since 24 Relations and Functions x-intercepts lie on the x-axis, we can ﬁnd them by setting y = 0 in the equation. Similarly, since y -intercepts lie on the y -axis, we can ﬁnd them by setting x = 0 in the equation. Keep in mind, intercepts are points and therefore must be written as ordered pairs. To summarize, Steps for Finding the Intercepts of the Graph of an Equation Given an equation involving x...
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