Functions

1. The following example represents a correspondence f from A to B. Determine whether the associated statements are true or false.

	i) One element of A corresponds to two elements of B.
	ii) Two elements of A correspond to the same element of B.
	iii) Some element of A has no corresponding element in B.
	iv) Some element of B has no element of A corresponding to it.
	v) Is f a function? If not, then explain why.

2. The following example represents a correspondence f from A to B. Determine whether the associated statements are true or false.

	i) One element of A corresponds to two elements of B.
	ii) Two elements of A correspond to the same element of B.
	iii) Some element of A has no corresponding element in B.
	iv) Some element of B has no element of A corresponding to it.
	v) Is f a function? If not, then explain why.

3. The following example represents a correspondence f from A to B. Determine whether the associated statements are true or false.

	i) One element of A corresponds to two elements of B.
	ii) Two elements of A correspond to the same element of B.
	iii) Some element of A has no corresponding element in B.
	iv) Some element of B has no element of A corresponding to it.
	v) Is f a function? If not, then explain why.

Determine whether each of the following table describe a function? Explain your reasoning.

4.

5.

6. Let f(x) = x² -3x +5. Find the following

i) f(2)
ii) f(1+ a)

7. Let f(x) = x² -3x +5. Find the following

8. Let f(x) = x² -3x +5. Find the following

9. Let the function f be defined by

i) Find f(1).
ii) Find f(3).
iii) Findf(-4).
iv) Sketch the graph of f.

10. Let the function f be defined by

Complete the following table.

Find the domain of each of the following functions
and express your answer in interval notation.

11. f(x) = x² -2x + 1.

^12.

^13.

^14.

15. For the graph of the function below, find

i) f(-2), ii) f(0), iii) f(1),
iv ) all x where f(x) = 0 , v) all x where f(x) < 1.

16. For the graph of the function below, find

i) f(0), ii) f(-1), iii) f(³/₂), iv) all x where f(x) = 1
v) all x where f(x)> 1