Algebra - Quotient Functions, Difference Quotients, Symmetry

Please see the attached file for the fully formatted problems.

Given and , which of the following is the domain of the quotient function ? Explain. 1._______

A.

B.

C.

D.

Find the difference quotient for f (x) = 3x - 7 and simplify. Show work.
A. 1 2._______

B. 3

C.

D.

Let . Which of the following is true? Give a brief explanation. 3. ______
A. f is an even function.
B. f is an odd function.
C. f is neither even nor odd.
D. f is both even and odd.

A graph of y = f (x) follows. No formula for f is given. 4. _______
Which graph (A, B, C, or D) represents the graph of y = f(x - 1) - 2 ?
BRIEFLY EXPLAIN how you have decided which graph is the correct one.
(Grid supplied for scratch work; You are NOT required to submit your own graph)

A. B.

C. D.

For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin?
(a)

Symmetric with respect to the
x-axis? ____ y-axis? ____ origin? ____
(b)

Symmetric with respect to the
x-axis? ____ y-axis? ____ origin? ____

(c)

Symmetric with respect to the
x-axis? ____ y-axis? ____ origin? ____
(d)

Symmetric with respect to the
x-axis? ____ y-axis? ____ origin? ____

(e)

Symmetric with respect to the
x-axis? ____ y-axis? ____ origin? ____
(f)

Symmetric with respect to the
x-axis? ____ y-axis? ____ origin? ____

Let f (x) = x2 - 5x + 2 and g(x) = x - 3.

(a) Find the difference (f - g)(x) and simplify the results. Show work.

(b) Find the composite function and simplify the results. Show work.

(c) Find . Show some work.

(d) Find the composite function and simplify the results. Show work.