Mth141S13n - Sec 1.3 Linear Functions Linear Functions...

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Sec. 1.3 – Linear Functions Linear Functions : Recall that y = m x + b is the general equation of a line with slope “m” and y-int “b”! We show a linear function by replacing “y” with f(x)! f(x) = mx + b The book defines a linear function as one of the form f(x) = ax + b, where a and b are real numbers. The key point here is that the exponent on the variable x is 1! The coefficient of the variable x is the slope of the line represented by y = ax + b. For graphing purposes, we replace the function notation, f(x), with y. If m = 0, we have a horizontal line y = b or f(x) = b. This is called a “constant” function. We saw an example, “ f(x) = 5 “ , of this in the last section. If m = 1 and b = 0, we have a 45 ° straight line called the identity function. f(x) = x. 1 5 2 8 \__________/ \ / \ Rule? / The rule is f(x) = x ! \_______/ 1 5 2 8 Is a horizontal line a function ? Yes! A constant function. Also try vertical line test! D R 1 2 3 4 2 Is a vertical line a function ? No! Also try vertical line test ! D R 2 1 2 3 4
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Graphing a linear equation:
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