MAT 171 Chapter 2 Review problems
1. Given the graph of y  f x  answer the questions below, using interval notation if possible.
a)
b)
c)
d)
e)
f)
What is the domain of f ?
What is the range of f ?
On what intervals is f increasing, decreasing and constant?
When does f x   0 , f x   7 ?
What is f 0 , f  5 ?
Find the coordinates of any local maxima and minima?
2. Using your calculator and the standard graphing window find the coordinates of the relative maximum and
relative minimum of the following graph.
(Give your answers correct to 2 decimal places)

y  .05 x 3  5x 2  36 x  50
7

3. Given g x    2 x  3
 x 2

a) Evaluate

 5  x  2
2 x 0
x0
g  3  6 g 0
2 g 3
b) Determine the domain of g x 
4. Given the following graph of y  f x  , find the equation for f x  . (Each square is one unit)
5. Given f x   x 2  3 and g x   2  x find  f  g  2 and  f  g 3
6. If f x   2 x 2  3x  1 find
f x  h   f x 
h
7. Given f x   x  2 and g x  
8. Given f x  
1
find g  f x  and it’s domain in interval notation
x 9
2
x
1
x 1
2
a) Describe any symmetries of f x  (symmetric about x axis, y axis, or the origin)
b) Is f x  even, odd or neither?
9. Know all of the transformations. (Given the graph of f x  below, tell how you would shift to obtain the
graph  2 f x  3  1). Graph  2 f x  3  1.
1
2 x  2

10. Graph the piecewise function. f ( x)   x
2 x  1


x  2
2  x 1
x 1