Name:
Period:
College Algebra- Ch.2 Test #2 (2.3 – 2.7)
C
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 3x is bent into the shape of a square. Express the area as a function of x.
1. ______(+2)
9 2
x
16
9
f ( x)  x 2
4
3
f ( x) 
x
16
f ( x)  3x 2
none of the above
A) f ( x ) 
B)
C)
D)
E)
2. Identify the domain of f ( x) 
A)
B)
C)
D)
E)
x
 x3
.
2. ______(+2)
(,3]
(,3]
(3, ), x  0
[3, )
none of the above
3. The point (9,3) on f ( x) 
A) (8,-3)
B) (10,-12)
C) (8,-124, 5)
D) (10,-3)
E) none of the above
x if transformed according to f ( x)  2 x  1  3 would end where?
4. A wire of length 2x is bent into the shape of a circle. Express the area A of the circle as a
function of x.
4x 2
A) A 
3. ______(+2)
4. ______(+2)

B) A  2x 2
x2
C) A 

D) A 
4x 2

E) none of the above
5. Find the average rate of change of f ( x)  3x 2  2 x from -2 to 4.
A)
1
4
B) 
1
4
C) 4
D) -4
E) none of the above
5. ______(+2)
6. A farmer has 600 feet of fencing to enclose a rectangular field. One side of the field lies along a river, so only
three sides require fencing. a) Express the area A of the rectangle as a function of x, where x represents the length
of each side perpendicular to the river.
6. _________________________(+5)
7. Determine the equation of the graph of f ( x)  x 3 reflected about the x-axis, shifted right 3, vertically stretched by
factor of 4, 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.
1
 3 x2

y   ( x  2) 2
 4


if
if
if

6  x  3 

3 x5


x5


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!
 x3
(a) f ( x)  2
(b f ( x)   x 3  4 x 2
12.(a) __________ (+2)
3x  9
(b) ___________(+2)
13. Let P = (x, y) be a point on the graph of y  x 2 . Determine the function d(x) as the distance d from P (x, y) to the
point (-2, 4) as a function of x. Simplify fully.
13. d(x) = ___________________________ (+5)
14. Find the average rate of change from -2 to x for f ( x) 
1
.
x3
14. _____________ (+5)
15. For f ( x)  3x 2  2 x  3 find the equation of the secant line (y=mx + b) containing (-2,f(-2)) and (1,f(1)).
15. _____________ (+5)
16. Identifying the intervals where the function is increasing, decreasing, or constant.
16. I: __________________(+1)
D: __________________(+1)
C: __________________(+1)
Domain __________________________(+1)
Range ___________________________(+1)
1)
17. Solve
2
4
x

 2
x  2 x  8 2 x  20 x  32
17. ___________________(+4)
18. Graph the function f ( x)   x  2  3 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
28x2 x  12  26 x(2 x  1)
____________________
___________________
____
_____
19.________________________________(+3)