Domain and Range Functions

1. State the range of each of the following functions a) f(x) = x + 8 ; D = { 1, 2, 3 } b) f(x) = x 3 ; D = { -2, -1, 0, 1, 2 } c) f(x) = (x-4) 2 ; D = { -1, 0, 1, 2 } d) f(x) = 4sinx ; D = { 0°, 30°, 60°, 90° } e) f(x) = 2cosx ; D = { 0°, 30°, 60°, 90° } f) f(x) = 3sinx ; D = { Real numbers } g) f(x) = x 2 ; D = { Real numbers } h) f(x) = 2x ; D = { 1, 2, 3 } i) f(x) = x 3 ; D = { Real numbers } ( In f,g,h and i above you may wish to sketch the graphs )

2.State the largest possible domain for each of the following functions. a) f(x) = √x b) f(x) = c) f(x) = d) f(x) = √ (x-4) e) f(x) = f) f(x) = g) f(x) = √ (2x-5) 3.Use a graphic calculator to draw the following curves. For each function state the range of the function. a) f(x) = x 2 b) f(x) = x c) f(x) = 6cosx d) f(x) = 2sinx e) f(x) = x 2 – 5 f) f(x) = sin2x g) f(x) = sinx + cosx

4. A car is traveling at v mph on a motorway and brakes suddenly. The stopping distance d of the car is given by What is the domain of d. Find the corresponding range of the function. 5.Draw the graph of the function on a graphic calculator. Determine the largest possible domain for this function.

6.State the domain and range for each of the functions shown in the diagrams  y = 6-x -2 7  9 y = 9-x (-5,2) -2 (-7,0) 3 (3,2) (8,6) (-2,4) y = x (-4,0) (5,-3) (-2,8) (10,5)