9 Questions for Examination 2 - College Algebra | MAT 140 | Exams Algebra

COLLEGE ALGEBRA - MAT 140

FALL 2008 - EXAM 2

Name :

TO RECEIVE FULL CREDIT YOU MUST SHOW YOUR WORK. No notes or books are allowed.

No. 1. (10 points) State whether each statement is True or False as stated. Provide a clear

reason for your answer.

i) A function can have more than one y-intercept.

ii) The graph of a function y=f(x) always crosses the y-axis.

iii) The y-intercept of the graph of the function y=f(x), whose domain is all real numbers, is

f(0).

iv) The domain of (f·g)(x) consists of the numbers xthat are in the domains of both fand g.

v) The average rate of change of a linear function f(x) = mx +bis the constant m.

No. 2. (6 points) Find the domain of the function f(x) = x

√x−4.

No. 3. (10 points) Determine whether the graph is of a function or not.

.....

−π−π

2π

−1

•• .....

−3−2−1 1 2 3

−3

−2

−1

.....

−3−2−1 1 2 3

−3

−2

−1

....

•

Figure 1:

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COLLEGE ALGEBRA - MAT 140

FALL 2008 - EXAM 2

Name :

TO RECEIVE FULL CREDIT YOU MUST SHOW YOUR WORK. No notes or books are allowed.

No. 1. (10 points) State whether each statement is True or False as stated. Provide a clear

reason for your answer.

i) A function can have more than one y-intercept.

ii) The graph of a function y = f (x) always crosses the y-axis.

iii) The y-intercept of the graph of the function y = f (x), whose domain is all real numbers, is

9 Questions for Examination 2 - College Algebra | MAT 140, Exams of Algebra

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Partial preview of the text

Download 9 Questions for Examination 2 - College Algebra | MAT 140 and more Exams Algebra in PDF only on Docsity!

COLLEGE ALGEBRA - MAT 140

FALL 2008 - EXAM 2

Name :

TO RECEIVE FULL CREDIT YOU MUST SHOW YOUR WORK. No notes or books are allowed.

No. 1. (10 points) State whether each statement is True or False as stated. Provide a clear

reason for your answer.

i) A function can have more than one y-intercept.

ii) The graph of a function y = f (x) always crosses the y-axis.

iii) The y-intercept of the graph of the function y = f (x), whose domain is all real numbers, is

f (0).

iv) The domain of (f · g)(x) consists of the numbers x that are in the domains of both f and g.

v) The average rate of change of a linear function f (x) = mx + b is the constant m.

No. 2. (6 points) Find the domain of the function f (x) =

x

x − 4

No. 3. (10 points) Determine whether the graph is of a function or not.

x

y

x

y

x

y

Figure 1:

No. 4. (16 points) Use the given graph of the function f , Figure 2, to answer parts (a)-(k).

x

y

Figure 2:

a) Find f (0) and f (6)

b) Is f (3) positive or negative?

c) For what numbers x is f (x) = 0.

d) For what numbers x is f (x) < 0.

e) What is the domain of f?

f) What is the range of f?

g) What are the x-intercepts?

h) What is the y-intercept?

i) How often does the line y = 1 intersect the graph?

j) How often does the line x = −2 intersect the graph?

k) For what value of x does f (x) = 3?

No. 6. (10 points) The monthly cost C, in dollars, of a certain cellular phone plan is given by

the function C(x) = 0. 38 x + 5, where x is the number of minutes used on the phone.

a) What is the cost if you talk on the phone for x = 50 minutes?

b) Suppose that your monthly bill is $29.32. How many minutes did you use the phone?

No. 7. (10 points) Suppose that a company has just purchased a new machine for its manufac-

turing facility for $120, 000. The company chooses to depreciate the machine using the straight line

method over 10 years.

a) Write a linear function that expresses the book value of the machine as a function of its age.

b) Graph the linear function

c) What is the book value of the machine after 4 years?

d) When will the machine be worth $60, 000.

No. 8. (10 points) For the data given in Table 1,

x 3 4 5 6 7 8 9

y 4 6 7 10 12 14 16

Table 1:

• Draw a scatter diagram on Figure 3.

• Use a graphing utility to find the line of best fit.

• Graph the line of best fit on the scatter diagram. (Free hand drawing not acceptable!)

x

y

Figure 3:

No. 9. (12 points) Match each graph to its function.

A. Square root function B. Cube function C. Reciprocal function

D. Absolute value function E. Square function F. Linear function

x

y

Figure 4: