Name:
Period:
MU
College Algebra- Ch.2 Test #2 (2.3 – 2.7)
In problems 1 - 5, choose the one alternative that best completes the statement or answers the question.
Supporting work/reasoning must be shown in order to receive credit for your answer.
1. A wire of length 22x is bent into the shape of a square. Express the area as a function of x.
1. ______(+2)
121 2
x
2
121 2
A
x
4
22 2
A
x
4
A  22x 2
none of the above
A) A 
B)
C)
D)
E)
2. Identify the domain of f ( x) 
A)
B)
C)
D)
E)
x  2
x
 2x  8
.
2. ______(+2)
(,4] and x  2
(,4)
All real but x  2
(, 2)
none of the above
3. The point (9,3) on f ( x)  x if transformed according to f ( x)  3  x  1  5 would end where?
A) (-8,-14)
3. ______(+2)
B) (-10,-12)
C) (-10,-4)
D) (-10,-14)
E) none of the above
4. A wire of length 10x is bent into the shape of a circle. Express the area A of the circle as a function of x.
25x 2

A  25x 2
5x 2
A

25x 2
A 2

none of the above
A) A 
B)
C)
D)
E)
5. Find the average rate of change of f ( x)  3 x 2  2 x  1 from -2 to 2.
A) -2
1
B) 
2
C) 2
D) -4
E) none of the above
4. ______(+2)
5. ______(+2)
6. A farmer has 1100 feet of fencing to enclose a rectangular field. One side of the field lies along a river and the
adjacent side borders a pond, so only two sides require fencing. a) Express the area A of the rectangle as a function of
x, where x represents the length of the side parallel to the river. Expand and simplify final answer.
6. ___________________________(+5)
7. Determine the equation of the graph of f ( x)  x reflected about the x-axis, shifted left 5, vertically stretched by
factor of 3, and then translated down 2.
7. _____________________ (+4)
8. Graph the following function (+3) and state the Domain/Range in interval notation. Label all transition and critical
points to receive full credit.



y



1
x2
4
x  2 1
7

8  x  4 

if 4  x  8


if x  8


if
D: _________________ (+1)
R: _________________ (+1)
Determine the functional equations of the following transformed graphs.
9. __________________ (+2)
10. _________________ (+2)
11. ________________ (+2)
(+1)
12. Determine algebraically whether the function is even, odd, or neither. Show work for all cases!
(a) f ( x) 
 5x
1 x2
(b
f ( x)   x 3  2 x
12.(a) __________ (+2)
(b) ___________(+2)
13. Let P = (x, y) be a point on the graph of y  2x 2 . Determine the function d(x) as the distance d from P (x, y) to
the point (-1, -3) as a function of x. Simplify fully.
13. d(x) = ___________________________ (+5)
14. Find the average rate of change from -3 to x for f ( x) 
1
.
x2
14. _____________ (+5)
15. For f ( x) 
x
find the equation of the secant line (y=mx + b) containing (-2,f(-2)) and (1,f(1)).
x 1
15. _____________ (+5)
16. Identifying the intervals where the function is increasing, decreasing, or constant. Give Domain and Range in
interval notation.
16. I: __________________(+1)
D: __________________(+1)
C: __________________(+1)
Domain __________________________(+1)
Range ___________________________(+1)
17. Determine the value(s) of x which make f(x)= -28 f ( x) 
6 x 2  42 x  12
x 1
17. ____________________(+4)
18. Graph f ( x)   x  4  2 using transformations. (+4) Start with the graph of the parent function and show all
stages. Label the stage represented below each graph. Label at least 3 points on each graph for full credit.
__________________
______
__________________
____________________
___________________
______
____
_____
19. Factor completely. Leave answer in fully factored form.
6 x 3 5x  12  8x 2 (5x  1)
19.________________________________(+3)