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3.2 Notes - Look at Example 6 on page 146 Find the domain...

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3.2 Introduction to Functions A function is a relationship between two variables (usually x and y), in which each value of x corresponds to exactly one y value. Think of a function as a machine that has been programmed with a certain rule. An input value is fed into the machine, and the machine performs the rule and the result is the output. Is the equation y = 3x + 2 a function? 8 6 4 2 2 4 6 8 10 5 5 10 Yes, because each x-value put into the equation gives a single y-value. Is the equation x = y² a function? 8 6 4 2 2 4 6 8 5 5 10 No, because if x=4 for example, y could be either 2 or -2
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Vertical Line Test If no vertical line can be drawn so that it intersects a graph more than once, the graph is the graph of a function. Look at Example 5 on page 145. Which of the following graphs are graphs of functions? The Domain of a graph or function is the set of x values. The Range of a graph or function is the set of y values.
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Unformatted text preview: Look at Example 6 on page 146. Find the domain and range of each graph. Write domain and range in interval notation. Function Notation Letters such as f and g are often used to name functions. When we write y = f(x), This means that y is a function of x (or y depends on x) y is called the dependent variable; x is called the independent variable The notation f(x) is read “f of x” (not f times x) Example: y = 4x + 3 can be written as f(x) = 4x + 3 The notation f(1) means to replace x with 1 and find the resulting value. f(1) = 4(1) + 3 f(1) = 7 This corresponds to the ordered pair (1,7) Find f(2) Find f(0) Find f(-1) F(2)=4(2)+3 f(0)=4(0)+3 f(-1)=4(-1)+3 F(2)=11 f(0)=3 f(-1)=-1 (2,11) (0,3) (-1,-1) Example: If g(x)=4x+5 and f(x)=3x²-x+2 Find a) g(0) b) g(-5) c) f(2) d) f(-1) Homework Ch. 3, asmt #3: p. 151 #23-81 odd (Bonus: 95,96)...
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