Name:
Period:
College Algebra- Ch.2 Test #2 (2.3 – 2.7)
D
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. Identify the domain of f ( x) 
A)
B)
C)
D)
x
x2
.
1. ______(+2)
(,2]
(,2]
(2, ), x  0
[ 2, )
E) none of the above
2. A wire of length 5x is bent into the shape of a square. Express the area as a function of x.
2. ______(+2)
5 2
x
16
25 2
B) f ( x) 
x
4
25 2
x
C) f ( x) 
16
D) f ( x)  5 x 2
A) f ( x ) 
E) none of the above
3. The point (4, 2) on f ( x) 
A) (-2,11)
B) (2,-11)
C) (6,-11)
D) (-6,11)
E) none of the above
x if transformed according to f ( x)  3 x  2  5 would end where? 3. ______(+2)
4. A wire of length 4x is bent into the shape of a circle. Express the area A of the circle as a
function of x.
4x 2
A) A 
4. ______(+2)

B) A  8x 2
16 x
C) A 
2

D) A 
16x 2

E) none of the above
5. Find the average rate of change of f ( x)  2 x 2  3x from -1 to 3.
A) -1
B) 
1
2
C) -2
D)
1
2
E) none of the above
5. ______(+2)
6. A farmer has 400 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 the side parallel to the river.
6. _________________________(+5)
7. Determine the equation of the graph of f ( x)  x 3 reflected about the x-axis, shifted right 2, vertically stretched by
factor of 5, and then translated down 3.
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.
 x3

y3

 x
3  x  0 

if x  0


if x  0

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!
1 x2
(a) f ( x)  x 3  4 x 2
(b f ( x) 
12.(a) __________ (+2)
x3
(b) ___________(+2)
13. Let P = (x, y) be a point on the graph of y  x 3 . Determine the function d(x) as the distance d from P (x, y) to the
point (-2, -8) 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4
14. _____________ (+5)
15. For f ( x)  2 x 2  5 x  2 find the equation of the secant line (y=mx + b) containing (-1,f(-1)) and (3,f(3)).
15. _____________ (+5)
16. Identifying the intervals where the function is increasing, decreasing, or constant. Also list domain and range
using INTERVAL NOTATION.
16. I: __________________(+1)
D: __________________(+1)
C: __________________(+1)
Domain __________________________(+1)
Range ___________________________(+1)
17. Solve
3
2
x

 2
x  3 x  4 2 x  14 x  24
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
16 x4 x  3  8 x 2 (4 x  3)
__________________
______
___________________
_____
2
19.__________________________(+3)