5. Given the function = 2 × 3x for 5, f(x) x –2 ≤ ≤ (a) find the range of f; (4) (b) find the value of given that = 162. x f(x) (2) (Total 6 marks) 6. (a) Factorize the expression 3x 10. x2 – – (2) (b) A function is defined as (x) = 1 + for x 3. f x3 x, –3 (i) List the elements of the domain of (x). f (ii) Write down the range of (x). f (4) (Total 6 marks) 7. The function = + is defined by the mapping diagram below. f(x) ax b (a) Find the values of andb. a (b) Write down the image of 2 under the function f. (1) (c) Find the value of c. (2) (Total 6 marks) 8. The following curves are sketches of the graphs of the functions given below, but in a different order. Using your graphic display calculator, match the equations to the curves, writing your answers in the table below. diagrams not to scale (Total 6 marks) Function Graph label (i) = + 1 y x3 (ii) = + 3 y x2 (iii) = 4 y x2 − (iv) = 2x + 1 y (v) = 3−x + 1 y (vi) = 8x 2x2 y x3 − − (a) : 3x is a mapping from the set to the set as shown below. 9. f x S T − 5
5. Given the function f(x) = 2 × 3x for –2 ≤ x ≤ 5, (a) find the range of f; (4) (b) find the value of x given that f(x) = 162. (2) (Total 6 marks) 6. (a) Factorize the expression x2 – 3x – 10. (2) (b) A function is defined as f (x) = 1 + x3 for x, –3 x 3. (i) List the elements of the domain of f (x). (ii) Write down the range of f (x). (4) (Total 6 marks) 7. The function f(x) = ax + b is defined by the mapping diagram below. (a) Find the values of a andb. (b) Write down the image of 2 under the function f. (1) (c) Find the value of c. (2) (Total 6 marks) 8. The following curves are sketches of the graphs of the functions given below, but in a different order. Using your graphic display calculator, match the equations to the curves, writing your answers in the table below. diagrams not to scale Function Graph label (i) y = x3 + 1 (ii) y = x2 + 3 (iii) y = 4 − x2 (iv) y = 2x + 1 (v) y = 3−x + 1 (vi) y = 8x − 2x2 − x3 (Total 6 marks) 9. (a) f : x 3x − 5 is a mapping from the set S to the set T as shown below.
quadratics_and_exponentials_ws.docx