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Dependent variable (y) – The 2 nd coordinate of ordered pairs; it is the variable that changes depending on the value of the 1 st coordinate Independent variable (x) – The 1 st coordinate of ordered pairs; it is the variable that changes independently of any other variable in the equation Constant – Any value that remains the same regardless of the variables The dependent variable y is a function of or is dependent on x. Because y is a function of x, it is expressed in symbols as y = f(x).

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Look at this example in the form of a chart. The relationship could also be expressed as f(t) = 60t since the distance is a function of, or is dependent on, the time if the rate remains constant. What is the domain of this relationship? Answer: Time is a non- negative number. It can be 0 seconds, 0.5 seconds, or any other positive rational number. The domain is {t: t ≥ 0}. What is the range of this relationship? Answer: The range depends on the values of t from the domain. If the values of the domain are substituted into the equation, the resulting values of f(t) or of d are {d: d ≥ 0}.

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2)Magnolia-Bell Telephone Company charges $0.50 for the first 2 minutes of a call, plus $0.10 for each additional minute. Write an equation to represent the relationship between the number of minutes talked and the total cost of the call. First define our variables. C = total cost of call m = time talked over original 2 minutes Now, write the equation: C = $0.50 + $0.10m or f(m) = $0.50 + $0.10m Next, organize the information in a chart:

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Notice in the chart how a change in the variable, m, resulted in a change in the variable, C. The cost of the initial 2 minutes talked, $0.50, remained constant in this example. Because m represented the independent variable, it becomes the 1 st coordinate (x) of the ordered pair. Likewise, because C represents the dependent variable, it becomes our 2 nd coordinate (y) of the ordered pair.

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What is the domain of this relationship? Answer: Time, or the number of minutes, is a non- negative number. It can be 0 seconds above the original 2 seconds, 0.5 seconds above the original 2 seconds, or any other positive rational number. The domain is {m: m ≥ 0}. What is the range of this relationship? Answer: The range depends on the values of t from the domain. If the values of the domain are substituted into the equation, the resulting values of f(t), or of d, are {C: C ≥ 0.50}.

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There are two primary methods for evaluating how the change in one variable affects another. Method 1: Substitute values of the independent variable and compare the change in the value of the dependent variable. Method 2: Analyze a graph. P. 251

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