Chapter Review 469 1. Find the real solutions, if any, of the equation + − = x x 2 1 0 2 2. Find an equation for the line with slope −3 containing the point ( ) −2, 5 . 3. Find an equation for a circle of radius 4 and center at the point ( ) − 0, 2. 4. Describe the equation − = x y 2 3 12. Graph it. 5. Describe the equation + − + − = x y x y 2 4 4 0 2 2 . Graph it. 6. Use transformations to graph the function ( ) = − + y x 3 2 2 7. Sketch a graph of each of the following functions. Label at least three points on each graph. (a) = y x2 (b) = y x3 (c) = y ex (d) = y x ln (e) = y x sin (f) = y x tan 8. Find the inverse function of ( ) = − f x x3 2. 9. Find the exact value of ( ) ( ) ° + ° − sin14 cos14 3 2 2 . 10. Graph ( ) = y x 3sin 2 . 11. Find the exact value of π π π − + tan 4 3cos 6 csc 6 . 12. Find an exponential function for the following graph. Express your answer in the form = y Abx. –6 –4 –2 2 4 6 4 6 8 y y 5 0 x 2 (1, 6) (0, 2) 13. Find a sinusoidal function for the following graph. –6 –3 3 6 –3 3 y x (–6, –3) (6, –3) 14. (a) Find a linear function that contains the points ( ) −2, 3 and ( ) − 1, 6 . What is the slope? What are the intercepts of the function? Graph the function. Be sure to label the intercepts. (b) Find a quadratic function with vertex ( ) − 1, 6 that contains the point ( ) −2, 3 . What are the intercepts of the function? Graph the function. (c) Show that there is no exponential function of the form ( ) = f x aex that contains the points ( ) −2, 3 and ( ) − 1, 6. 15. (a) Find a polynomial function of degree 3 whose y-intercept is 5 and whose x-intercepts are −2, 3, and 5. Graph the function. (b) Find a rational function whose y-intercept is 5 and whose x-intercepts are −2, 3, and 5 that has the line = x 2 as a vertical asymptote. Graph the function. Cumulative Review Cumulative Review
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