Reference no: EM131018976

1. A student was given the function f(x) = x² and asked to write the result of translating this function 1 unit to the left. The student wrote the following: g(x) = (x+1)². Is this statement correct? Explain

2. The length of time that it takes for a pendulum to make one complete swing depends on the length of the pendulum. The time in seconds, T, is related to the length in metres, L, through the equation T = 2 π√(L/9.8)

a) Write this equation in function notation.

b) State the domain and range of this function.

c) Graph this function for pendulums up to 20m in length.

d)  If you wanted to construct a pendulum in the Ontario Science Centre that takes exactly 10s to complete one swing, how long would it have to be (to the nearest millimetre)?

e)  What would be the effect on the value of T if the pendulum were made twice as heavy?

3. A student was asked to find the inverse of the function f(x) = 3x - 7. The student began the solution with the following:

f(x) = 3x - 7 as y = 3x - 7

∴ x = 3y - 7

The student eventually obtained the correct equation for f^-1(x) but did not get full marks for the solution. Why not?

4. For the following graph

a) State as accurately as possible the intercepts, maximum and minimum values, the domain and range, and the intervals in which the function is increasing or decreasing.

b) Explain why the inverse of this is or is not a function.

5. Determine the domain and range for each function given. Explain where any restrictions come from.

f(x) = √(x+5) - 4

f(x) = 1 / (2x² -32)

f(x) = 4 / (x² +1)

6. Determine the inverse for each relation given.

a. f(x) = {1 / (x-2)} + 3

b. f(x) = 2(x - 4)² + 5

7. Graph each relation and its inverse from question 6, indicate which relations are functions and explain why or why not.