Math 131 Week in review 1
I. Classify each function as a power function, a polynomial, a rational function, or an exponential
function and find f(a) for the given a.
a ) f ( x )  5 (3 )
a2
c) g ( x)  6 3 x
a  8
x
b) f ( x)  4 x
d ) h( x) 
e ) K ( x )  18 x  24 x  32
5
a2
3x  5
x  9x  4
2
a 1
a  2
3
II. What are the domain and range of a function?
Find the domain and range of each function.
a)
f ( x) 
x2
b)
f ( x) 
x 1
2
c)
f ( x) 
x 1
2
WIR
d)
g ( x) 
x
x  3x  4
2
1. A box will be made from a 50 inch by 20 inch cardboard by cutting equal size squares from the
corners. Describe the volume of the box as a function of the side of the square cutouts.
2. Simplify the difference quotient
f ( x  h)  f ( x)
h
2
for f ( x )  x  3 x .
3. A box has a rectangular base with length equal to twice the width. The height of the box is 1.5 times
the length. Describe the volume as a function of the width.
f ( x) 
4. Find the domain of a )
2
x  3x  2
b)
1
g ( x) 
16  x

2
25  x
5. Graph the piecewise function f ( x )  

2
5 x0
0 x
3x
What is the domain of f?
Where is f increasing? Where is f decreasing?
6. Determine whether or not the points are collinear? What is the least squares best fitting line? Are any
of the original points on the least squares line?
a) (-3, 4) (0,1) (2, -2.5)
b) (0, 1) (1, 3) (2, 4.2) (3, 5.6)
7. Factor each quadratic and find any roots or state no roots exist.
2
a)
y  x  3x  2
d)
y  x  6 x  10
2
y  2x  3x  2
b)
2
e)
c)
2
y  9 x  12 x  5
2
y  16 x  8 x  1
8. Find the degree and leading term and leading coefficient of each polynomial.
a)
7
24  x  4 x
3
b)
8
5 x  7 x  90
9. For y   4 x  5 ,
a) if x increases by 1 unit then y___________.
b) if x decreases by 2 units the y___________.
c) if y increases by 3 units then x______________.
10. A tree is 2.4 ft tall when planted. It’s height increases by 50% the first year and increases by 70% the
second year.
a) Describe the height of the tree using a piecewise linear model.
b) Use quadratic regression to find a quadratic model. What does the value of r 2 tell you in this case?
11. An object is shot upward into the air with velocity v ( t )  20  10 t cm./sec where t is in seconds.
When is the velocity positive, 0, negative?
When is the height increasing, stationary, decreasing?
12. Each function is a transformation of a basic function. Give the basic function and list the
transformations in a proper order that result in the given function.
a)
f ( x)  2 x  5  6
b)
f ( x )  2 cos( x 

)
4
c)
f ( x )  ( x  2 )( x  6 )
d)
f ( x )  15  x  2 x
2