Graphing Transformed Functions Homework PDF

1. State the transformations defined by each equation in the order that they would be applied to y = f ( x). 1 1  a. y = −2 f (4 x) b. y = − f ( x − 3) + 2...

1. State the transformations defined by each equation in the order that they would be applied to y = f ( x). 1 1  a. y = −2 f (4 x) b. y = − f ( x − 3) + 2 c. y= f  x + 5 − 6 2 4  2. Draw an accurate graph of each of the following functions. 1 a. y = − ( 2( x − 1) ) + 5 b. y = x + 2 −3 2 c. y = 3 −x + 5 +1 2 2 1 d. y = +2 e. y = − | x + 3 | −5 f. y = − x −1 + 5 4− x 4 3. Given each of the following functions below, graph y = − f (−2 x + 8) + 3 1 a. f ( x) = x 2 b. f ( x) = x c. f ( x) =| x | d. f ( x) = x 4. Graph each piecewise function. | x | x  −2  − x − 1 x  −1 a. f ( x) =  2 b. f ( x) =  2 − x x  2 − x + 2 x  −1  −( x + 5) + 4 x  −3 2 1  x 1  c. f ( x) =  x d. f ( x) = 3 x + 3 −3  x 1  x x 1  1  +5 x 1 x−2 5. Write the equation for each piecewise function. a. b. 6. The graph of y = f ( x), consisting of two line segments and a semicircle, is shown for −3  x  5. Sketch a graph of g on the same axes where: a. g ( x) = f ( x + 3) − 4 b. g ( x) = − f (2 x) + 1 c. g ( x) = 3 f (−0.5 x − 1) + 2 7. The three graphs below show the complete graph of a function y = f ( x). a. Is f ( x ) an odd function, even function, or neither? Explain b. On the first graph, sketch y = g ( x), where g ( x) = − f ( x) c. On the second graph, sketch y = h( x), where h( x) = f (− x − 2) d. On the third graph, sketch y = w( x), where w( x) = 2 f (− x) + 1 e. f ( x ) passes through the points A (0, –2.4), B (2, 0) and C (5, 1). Give the coordinates of the images of these three points on the graphs of g, h, and w.