MTH: 160 COLLEGE ALGEBRA
Chapter 2 Review
NAME_________________________
Please show all your work on this test and simplify all answers.
Please place a box around your final answer.
1)
Test algebraically whether the graph is symmetric with respect to the x-axis, the y-axis,
and/or the origin. Please state yes or no for each.
y 2  x3  2 x
x  axis ?__________________ y - axis ?____________________ origin ?___________________
2)
Write an equation for a function that has the shape of y  x , but shifted left 3 units and
up 4 units.
3)
Write an equation for a function that has a graph with the shape of y  x 2 , but shifted right
6 units and up 2 units.
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 x  5, for x  1


4) Graph: f ( x )   x 2 , for -1  x  2 
 - x , for x  2 


5) For f ( x )  x 2  1 and g ( x )  36  x 2 , find
a) the domain of f ( x ) , using interval notation;
b) the domain of g ( x ) using interval notation;
c) (f o g)( x ) ;
d) (g o f)( x )
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6)
A rancher has 360 yd of fencing with which to enclose two adjacent rectangular corrals,
one for the sheep and one for cattle. A river forms on side of the corrals. Suppose the
width of each corral is x yards.
a)
b)
c)
7)
Express the total area of the two corrals as a function of x .
Find the domain of the function.
Maximize the area and give the length and width.
For the pair of functions, f ( x )   x  1 and g ( x )  4 x  2 find the following:
a. (f  g )( x )  __________________________________
b. (f  g )( x )  __________________________________
c) (fg )( x )  ____________________________________
d) (f / g )( x )  __________________________________
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8)
Determine the intervals on which the function is (a) increasing, (b) decreasing, and (c)
constant:
a. _________________________
b. _________________________
-5
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c. _________________________
9) Variation
a) According to Fidelity Investments Investment Vision Magazine, the average weekly
allowance A of children varies directly as their grade level G. It is known that the
average allowance of the 5th grade student is $5.88 per week. What then is the
average allowance of a 9th grade student?
b) The weight W of an object varies inversely as the square of the distance d from the
center of the earth. At sea level (3978 mi from the center of the earth), an astronaut
weighs 220 lbs. Find his weight when he is 200 mi above the surface of the earth.
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10) Graph each equation and determine whether each graph is that of a function. State the
domain and the range of each using interval notation.
.
a) y   ( x  3)  5
b) y  (4  x) 2  2
a) Function: Yes?__________No?_________
Domain?__________________
Range?___________________
b) Function: Yes?__________No?_________
Domain?__________________
Range?___________________
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