Math-130-Exam #2
Practice Exam
Name___________________________________
Date: _____________________
Instructions: Show all work neatly. Answers without support will receive no credit. Your answers will be evaluated on
the correctness, completeness and use of mathematical concepts we have covered. Box your final answer and write your
answers in the answer column when possible.
Find the value for the function.
1) Find f(x - 1) when f(x) = 2x2 - 5x + 7.
1)
Solve the problem.
2) If a rock falls from a height of 100 meters on Earth, the height H (in meters) after x seconds
is approximately
H(x) = 100 - 4.9x2 .
2)
What is the height of the rock when x = 1.4 seconds? Round to the nearest hundredth, if
necessary.
Find the domain of the function.
3) f(x) = 7 - x
3)
Find and simplify the difference quotient of f,
f(x + h) - f(x)
, h 0, for the function.
h
4) f(x) = 4x + 6
4)
5) f(x) = 8x2
5)
The graph of a function f is given. Use the graph to answer the question.
6) Use the graph of f given below to find f(40) and f(-50). Determine whether the graph is the
graph of a function. Find the domain and range. Find f(x) = 0 and f(x) = -20.
50
50
-50
-50
1
6)
The graph of a function is given. Determine the interval where the function is increasing, decreasing, or constant. Find
the local minimun and local maximum.
7)
7)
Find the average rate of change for the function between the given values.
8) f(x) = x2 + 6x; from 3 to 8
Graph the function.
9) f(x) = x - 1
4
if x < 1
if x 1
8)
9)
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
10) f(x) = (x + 1)2
10)
2
11) f(x) =
11)
x+1-1
12) f(x) = 6x2
12)
Find the requested function value.
13) Find (f
g)(-6) when f(x) = 9x + 2 and g(x) = -9x2 - 2x + 1.
For the given functions f and g , find the indicated composition.
g(x) = 2x - 1
14) f(x) = 3x + 14,
(f g)(x)
Determine whether or not the function is one-to-one.
15)
13)
14)
15)
3
If the function is one-to-one, find its inverse. If not, write "not one-to-one."
16) f(x) = -7x + 1
17) f(x) = x3 - 3
16)
17)
Find the domain and the range of the relation. Use the vertical line test to determine whether the graph is the graph of a
function.
18)
18)
4
Answer Key
Testname: MATH-130-E2-F15-PRACTICE
2x2 - 9x + 14
90.4 m
{x|x 7}
4
8(2x + h)
f(40) = 20
f(-50) = 30
It's a Function
Domain: [-50, 50]
Range: [-40, 50]
f(x) = 0
x=-30 and x 35 and x =50
f(x) = 20
x =-25 and x = 30
7) increasing on Interval: (-1, 0) (1, 3)
decreasing on Interval: (-3,1) (0, 1)
local max at the points (-3, 3), (0, 2) and (3,3)
local max at the points (0,-1) and (0,1)
8) 17
9)
1)
2)
3)
4)
5)
6)
10)
5
Answer Key
Testname: MATH-130-E2-F15-PRACTICE
11)
12)
13) -2797
14) 6x + 11
15) No
1
1
16) f-1 (x) = - x +
7
7
3
17) f-1 (x) = x + 3
18) domain: (- , )
range: [-6, )
function
6