Math 3
Chapter 2 Quiz
Name___________________________________
Complete, organized, and correct work using the methods taught in class and including correct use of symbols is required
for full credit. Partial or no credit will be given when work is missing. Each problem is worth 5 points.
SHOW ALL WORK . DO NOT ROUND ANSWERS UNLESS INSTRUCTED TO DO SO. Leave final answers in
simplified form.
time: 20 minutes
Determine whether the relation is a function. Explain how you determined your answer.
1)
The graph does represent a function because a vertical line will pass through only one point at a time.
2) {(-6, -9), (-5, -1), (-1, 3), (2, -1)}
Yes, the relation is a function because each x-value has a unique y-value.
Determine whether the equation defines a function. Explain how you determined your answer.
3) y = -18
Yes, the relation is a function because each x-value has a unique y-value.
Find the domain and range.
4) y = 2 + x
2+x 0
x -2
Domain [- 2, )
Range [0, )
Evaluate.
5) If f = (1, -4), (4, -1), (6, 3) and g(x) = 7x + 6, find f(4) + g(4).
f(4) + g(4) = - 1 + 7 4 + 6
= - 1 + 28 + 6
= 33
1
Find the difference quotient for the function and simplify it.
g(x + h) = 8(x + h)2 + 12(x + h) - 13
6) g(x) = 8x 2 + 12x - 13
= 8 x 2 + 2xh + h 2 + 12x + 12h - 13
= 8x 2 + 16xh + 8h 2 + 12x + 12h - 13
8x 2 + 16xh + 8h 2 + 12x + 12h - 13 - 8x 2 + 12x - 13
h
difference quotient =
=
16xh + 8h 2 + 12h
h
= 16x + 8h + 12
BONUS. Find the difference quotient for the function and simplify it. (6 POINTS)
7) p(x) = 3 - 5x 3
p(x + h) = 3 - 5(x + h)3
p(x + h) = 3 - 5 x 3 + 3x 2h + 3xh 2 + h 3
p(x + h) = 3 - 5x 3 - 15x 2h - 15xh 2 - 5h 3
difference quotient =
difference quotient =
3 - 5x 3 - 15x 2h - 15xh 2 - 5h 3 - 3 - 5x 3
h
-15x 2h - 15xh 2 - 5h 3
h
difference quotient = -15x2 - 15xh - 5h 2
2