Wk3EYB_Final_Solutions.docx

Wk3EYB_Final_Solutions.docx - W3.1 Group Members who worked...

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W3.1 Group Members who worked on this problem: Jessica In the following functions, a basic common function, f(x), has undergone a transformation into another function. For each of the following graphs, determine the equation for g(x). f ( x ) = x 2 a. g(x) = b. g(x) = c. g(x) = Calculations Explanations of Calculations 1 a.) f ( x ) = x 2 g(x) = x 2 + 5 g(x)= x 2 + 5 = f ( x ) + 5 f ( x ) = x 2 is the first graph. Then when you look at the graph a.) you can see it is the same except the line has shifted up the y-axis by 5 spaces. So we write g(x) = x 2 + 5 = f(x) + 5 Example Figure 2.43 Verticle Shifts Chapter 2.5 pg. 255 b.) f ( x ) = x 2 g(x) = (x - 6) 2 g(x) = (x – 6) 2 = f(x – 6) Just like above f(x) = x 2 is the original graph. Then graph b.) shows a horizontal shift to the right (x-axis) by 6 spaces. So g(x) = (x – 6) = f (x – 6) (To the right would make a subtraction equation and to the left would be addition.) Example Figure 2.44 Horizontal Shifts Chapter 2.5 pg. 257
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C,) f ( x ) = x 2 g(x) = -x 2 g(x) = -x 2 = -f(x) In graph c.) it is a reflection about the x- axis g(x) = -x 2 mirrors f(x)=x 2 The graph of y = -f(x) is the graph of y = f(x) reflected about the x-axis. Example Figure 2.45 Reflection about the x-axis Section 2.5 pg. 259 (Add or delete rows as needed). W3.2 Group Members who worked on this problem: Jessica Find the domain for the following functions. You may use either set-builder notation or interval notation.
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