Function Revision Questions

1. Sketch the graph.
a.) y = log2x (1 mark)
b.) y = log2(2)x (2 marks)

2. f(x) = 3 - x and g(x) = 3/x , x ≠ 0
a.) Find p(x) where p(x) = f(g(x))   (2 marks)
b.) If q(x) = 3 / (3-x) , x ≠ 0, find p(q(x)) in its simplest form.  (3 marks)

3. Using the graph y = log2x from question 1.
a.) If the coordinates were (a,0) and (8,b), state the values of a and b.  (1 mark)
b.) Sketch the graph of y = log2(x +1) - 3  (3 marks)

4. Using the graph y = sinx, sketch the graphs of:
a.) y = sin(x+1) (1 mark)
b.) y = -2sin(x)  (1 mark)

5. f(x) = 2x - 1, g(x) = 3 - 2x and h(x) = 1/4 (5 - x)
a.) Find a formula for k(x) where k(x) = f(g(x))  (2 marks)
b.) Find a formula for h(k(x))                             (2 marks)
c.) What is the connection between the functions h and k? (1 mark)