Math253
Practice Exam #04
1. Find any x-intercepts and y-intercepts for the parabolic functions. If no x-intercepts exist, write
down “no x-intercepts”.
a)
f ( x) =
− x2 + 2 x + 3
b) g ( x ) = 2 x 2 − 4 x + 6
2. For each of the parabolic functions, find the coordinates of the vertex. Also state whether the
parabola opens upward or downward.
b)
f ( x ) =x 2 − 10 x + 21
b) g ( x ) =
−2 x 2 + 8 x − 2
3. A furniture builder is designing a rectangular end table with a perimeter of 128 inches. Which
dimensions will give the end table the maximum area?
Be sure to show your work. No credit will be given if you just write down the dimensions.
Recall:
P=
2l + 2 w
A=
lw
w
l
4.
Solve the inequality and write your answer using interval notation.
a)
( x − 3)( x + 2 ) ≥ 0
5. Given the functions below, first find
a)
f ( x ) = x2
g ( x )= x + 1
b) x ( x − 4 )( x + 5 ) < 0
( f  g )( x ) . Next find ( f  g )( 4 ) .
b)
f=
( x)
g (=
x)
6x − 8
3
x2 − 2x
6. Sketch a graph of each exponential function and define its Domain and Range.
a)
f ( x ) = 3x
b) f ( =
x ) 2− x − 4
7. Evaluate each logarithm.
a) log 5 25
b) log 2 8
c) log 4 2
1
d) log 3  
9
e) log 5 1
f) log 9 27
h) log 3 0
i) log8 4
g)
log x 3 x
x>0
8. Solve each equation for x.
a) log 3 x = 4
b) log x 8 = 3
9. Solve each equation for x
a) 22 x = 8
4
c) log 2 ( x − 3) + log 2 ( x + 3) =
b) log 2 ( 8 − 6 x ) =
4
Math253
Exam #04 Solutions Fall 2016
1. Find any x-intercepts and y-intercepts for the parabolic functions. If no x-intercepts exist, write
down “no x-intercepts”.
a)
f  x    x2  2x  5
b) g  x   2 x 2  4 x  6
2. For each of the parabolic functions, find the coordinates of the vertex. Also state whether the
parabola opens upward or downward.
b)
f  x   x 2  12 x  20
b) g  x   2 x 2  12 x  3
3. A gardener has 100 feet of fencing to fence in a rectangular rose garden where a wall forms one
side of the rectangle. Which dimensions will give the rose garden the maximum area?
Be sure to show your work. No credit will be given if you just write down the dimensions.
l
w
Rose Garden
Wall
w
4. Solve the inequality and write your answer using interval notation.
a)
 x  3 x  2  0
5. Given the functions below, first find
a)
f  x   2 x3
g  x  1 x
b) x  x  3 x  5  0
f
g  x  . Next find  f g  3 .
b)
f  x   3 x 2  2 x  12
g  x   x 2  3x  7
6. Sketch a graph of each exponential function and define its Domain and Range.
a)
f  x    2 x
b) f  x   3x2  2
7. Evaluate each logarithm.
a) log 2 32
b) log3 27
c) log8 2
1
d) log 4  
 16 
e) log9 1
f) log 27 9
g)
log 4 3 4
h) log x 1
x0
1
i) log8  
 16 
8. Solve each equation for x.
a) log 4  x  3  3
b) log x 8 
1
3
9. Solve each equation for x
a)
2x
4

1
8
c) log3  2 x 2  3x  75  4
b) log8 8  6 x  
1
2
Fall 2016