College Algebra
Unit 3 Take-Home Quiz
Due: Odds – Thursday November 10th
Evens – Friday November 11th
Name
Directions: Show all work and reasoning to receive full credit.
For Questions 1 & 2, determine algebraically whether the function is even, odd, or neither. Then state any
symmetry.
 x3
3
1) f ( x)  2
2) g ( x)  3 x 2  8
4x  9
3) Use the graph to the right to answer the following questions a - f.
a) Determine the interval when the function is
increasing.
b) Determine the interval where the function is
constant.
c) Determine the interval where the function is decreasing.
d) List the intercepts (x, y) for the function.
e) Find f(3).
f) For what value of x does f(x) = -2?
4) Find the average rate of change of the function f (x) 

x3
from -3 to 2.
x2  3
5) Use the function f ( x)  x 2  7 x to answers questions a and b.
a) Find the average rate of change from -1 to x.
b) Find the equation of the secant line in slope intercept form containing (-1, f(1)) and (2, f(2)).
6) Write a rule for piecewise function graphed.



f ( x)  



1
1
8) Graph by hand the following function.
List the sequence of transformations.
1
f ( x)   x  2  3
2
1
7) Graph the given piecewise function.
 1
 2 x  2, (, 2]

 1
f ( x)   x 2  3, (2, 4]
 2
 3x  13, (4, )


9) Graph by hand the following function.
List the sequence of transformations.
g ( x)  2  x  3  1
1
1
1
1
1
10) Determine the equation of the following graph.
1
11) Determine the equation of the following graph.
1
1
1
12) A wire of length 5x is bent into the shape of a square. Express the area as a function of x.
13) Let P = (x, y) be a point on the graph of y  x 2 -1. Determine the function d(x) as the distance d from P (x, y) to the
point (-2, 3) as a function of x. Simplify fully.