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CHAPTER 2 SECTION 1
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Basics of Functions and Their Graphs
Goal: find domain and range, determine if a relation is a function, determine if an equation is a function, evaluate a function, graph a function, use the vertical line test, interpret graphs, and find intercepts. A relation is any set of ordered pairs. {(2,7),(-3,5),(4,-2),(1,9),(-4,5)} The domain is the set of x-values. The range is the set of y-values.
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A function is a correspondence from the first set, called the domain,
to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range. Determine if each relation is a function: Determining if a relation is a function: Do any of the x-values repeat? no, then the relation is a fucntion yes, go to step two If an x repeats, does it have the same y value? yes, then the relation is a function. no, then the realation is not a function. {(2,5),(-1,9),(8,12),(-5,0)} {(2,9),(-3,7),(2,9),(12,5)} {(12,0),(3,4),(0,7),(3,-4)}
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Determining Whether an Equation Represents a Function.
1. x2 + y = 4 Solve each equation for y and determine if the equation has multiple values for x at a given y. 2. x2 + y2 = 16
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Evaluating a Function f(x) = x2 + 3x + 5 f(2) f(x + 3) f(-5) f(-x)
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Graphing Functions f(x) = 2x f(x) = x2 – 5 f(x) = │x│ + 3
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Vertical Line Test If any vertical line intersects a graph in more than one point, then the graph does not define y as a function of x. 1. 2.
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3.
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Analyzing the graph of a function, Domain and Range:
Is f(x) a function? Explain. Estimate f(5) For what value is f(x) = 3 What is the domain? What is the range?
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HOMEWORK PAGE {2-6,12-18,28-32,40-46,52-64} EVENS {65-80} ALL
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