Math 131
Graph Reading
Section 2.2
In the following problems there are no formulas given for the functions. Since you will be
reading from graphs, your answers will be approximations.
1. The graph below is of the function y  f  x  .
Evaluate the following:
40
32
24
16
8
0
0
1
2
3
(a) f  3
4
5
(b) f  3  5
(d) f 11  f  7 
f 1  h   f 1
when h  5
h
1
(h)
when x  2
f  x
Find x when:
(j) f  x   30
(m) f is increasing
(f)
Determine:
(o) Domain
6
7
8
9
10
11
(c) f  3  f  5
(e)
f b  f  a 
when a  7 and b  11
ba
(g) 3 f  x  1  100 when x  4
1
(i) f   when x  2
x
(k) f  x   20
(n) f is decreasing
(l) f  x   24
(p) Range
Challenge Question: Draw a graph of a function that has a Domain of  2,9  and a Range of
8,32 .
Math 131
Graph Reading
Section 2.2
2. Below are the graphs of f and g.
6
6
Graph of f
Graph of g
3
3
0
0
(a)
-3
-5
-4
-3
-2
-1
0
1
2
3
4
Evaluate g  0 , f  0  , f  4  , and g  4 .
5
-3
-5
(b) Find x when g  x   0 .
(c) Evaluate f  2  g  2 .
(d) Find x when f  x   g  x  .
(e) When x  3 , find f   x  and  f  x  .
(f) Find when f is decreasing. Find when f is decreasing.
(h) Find when both f and g are decreasing.
(i) Find when f  x   0 .
(j) Find when g  x   0 .
(k) Find when both f  x   0 and g  x   0 .
(l) Find the domain and range of f.
(m) Find the domain and range of g.
-4
-3
-2
-1
0
1
2
3
4
5
Math 131
Graph Reading
Section 2.2
3. The graphs below are the distance vs. time for two remote-controlled cars, car A and car B,
racing around a track. We denote their position functions by A  t  and B  t  , respectively.
(a) Find how far car A traveled during the first 7 seconds.
32
A(t)
28
Distance (feet)
24
20
B(t)
16
12
B(t)
8
4
A(t)
0
0
1
2
3
4
5
6
Time (seconds)
(b) Find B  6 .
(c) Find when car B traveled 20 feet.
(d) At what time(s) do they meet?
(e) Find all times for which car A is ahead of car B.
(f) Find all times for which car B is ahead of car A.
(g) Find A  7   B  7  .
(h) Find a time when car B is 4 feet ahead of car A.
(i) Find a t when A  t  2  B  t  .
(j) Find a t when A  t   B  t   10 .
(k) Which car won the race?
(l) Which car traveled faster during the last 2 seconds?
7
8
9
10