MAC 1105C Final Exam Review: Get Answers to Ace Your Quiz

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the domain of the function f(x) = |x - 5|?

(-5, ∞)

[0, ∞)

(-∞, ∞) (correct)

(-5, 5)

What is the graph of the function g(x) = -x + 2 + 1?

Graph B

Graph C

Graph D

Graph A (correct)

Which of the following functions has an inverse function?

Graph B

Graph C (correct)

Graph A

Graph D

What is the value of x that satisfies the equation 3^4x - 1 = 6?

1/4 Signup and view all the answers

What is the solution to the inequality -2 < 21 - 2y < 10?

(-11/2, 2) Signup and view all the answers

What is the domain of the function f(x) = 3 - x?

(-∞, 3) Signup and view all the answers

What is the value of ln e^(6/5)?

6/5 Signup and view all the answers

What is the solution to the equation |3x - 2| = 5?

{-1, 7} Signup and view all the answers

What is the value of x in the solution to the system of equations 3x - y = 5 and 2x + 3y = -4?

1 Signup and view all the answers

What type of symmetry does the graph of 7y^2 = 4x^3 - 5 possess?

No symmetry Signup and view all the answers

What is the equation that can be used to determine how long it will take a $1000 investment to double if it is invested at 6% interest compounded continuously?

2000 = 1000e^(0.06t) Signup and view all the answers

What is the accumulated value of an investment of $5000 after 10 years at an interest rate of 6.3% if the interest is compounded continuously?

$9388 Signup and view all the answers

Which of the following is the correct graph of the function f(x) = log2(x-1)?

Graph C Signup and view all the answers

What is the value of the expression log7(59) in terms of a and b?

log7(9) - 4log7(a) + log7(b) Signup and view all the answers

What is the inverse of the function f(x) = 2x - 3?

f^-1(x) = x + 3 Signup and view all the answers

What is the value of the expression f(x + h) - f(x) / h when f(x) = 2x^2 - 2x + 1?

4x + 2h + 2 Signup and view all the answers

What is the solution to the equation 3ln(4x) = 6?

e^2 Signup and view all the answers

What are the x-intercepts of the graph of the function f(x) = 3x^2 - 2x + 1?

(-1, 0) and (3, 0) Signup and view all the answers

What is the value of log3(81x2) in terms of log3x?

4 + 2log3x Signup and view all the answers

What is the value of logb(y - 4x - z) in terms of logb(y), logb(x), and logb(z)?

logb(y) - 4logb(x) - logb(z) Signup and view all the answers

What is the value of (gf)(4) if f(x) = logb(x) and g(x) = x + 12?

9/8 Signup and view all the answers

What is the graph of the function f(x) = 2^{-x}?

an exponential decay Signup and view all the answers

What is the value of f(-1) if f(x) = 2x + 3 for x ≤ -1 and f(x) = 1 - 5x for x > -1?

6 Signup and view all the answers

What is the equation of the asymptote for the graph of f(x) = 2x + 3?

y = 3 Signup and view all the answers

What is the quadratic equation that needs to be solved in the process of solving the radical equation x − 5 = 3x − 11?

x² - 7x + 16 = 0 Signup and view all the answers

Which of the following relations defines y as a function of x?

{(0, 4), (4, 0), (0, -4), (3, 0)} Signup and view all the answers

What is the distance between the points (5, 4) and (1, -1)?

√41 Signup and view all the answers

What is the symmetry of the graph shown below, and what type of function does it represent?

y-axis, even Signup and view all the answers

What is the revenue generated by selling 10 items, according to the function p(x) = -x² + 26x + 300?

$660 million Signup and view all the answers

What is the maximum revenue that the company may achieve for sales of the item, according to the function p(x) = -x² + 26x + 300?

$807 million Signup and view all the answers

Study Notes

Logarithms and Exponents

log3 ( 81x 2 ) can be expressed in different ways: log3 ( 81 ) + 2log3 x, 4 + 2log3 x, log3 ( 81 ) - 2log3 x, log3 ( 81/x 2 ), or 4log3 x
The formula logb y - logb x - logb z is equal to logb (y/xz)
f(x) = 2^(-x) and g(x) = x have a composite function (gf)(x)

Graphs and Functions

f(x) = 2^(-x) has a graph that is a reflection of y = 2^x across the y-axis
f(x) = x^2 + 4 is an even function, meaning f(-x) = f(x)
f(x) = x^3 + 4x is an odd function, meaning f(-x) = -f(x)
y = f(x) - 3 has a graph that is a vertical translation of y = f(x) down 3 units

Exponential Equations

ln(5t + 1) - ln(t + 2) = ln 3 can be solved by using the properties of logarithms
log x + log(2x + 1) = 1 can be solved by using the properties of logarithms
2^(x-2) - 3 = 0 can be solved by using the properties of exponents

Inequalities

2x - 5 < 3 can be solved by adding 5 to both sides and then dividing both sides by 2
-2 < 21 - 2y < 10 can be solved by adding 2y to all parts of the inequality and then dividing all parts by 2

Systems of Equations

3x - y = 5 and 2x + 3y = -4 can be solved by using substitution or elimination methods

Compound Interest

The formula A = Pe^(rt) can be used to calculate the accumulated value of an investment, where A is the accumulated value, P is the principal, r is the interest rate, and t is the time in years
The formula A = P(1 + r/n)^(nt) can be used to calculate the accumulated value of an investment with compound interest, where A is the accumulated value, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years

Symmetry and Graphs

A graph is symmetric with respect to the x-axis if f(-x) = f(x)
A graph is symmetric with respect to the y-axis if f(x) = f(-x)
A graph is symmetric with respect to the origin if f(-x) = -f(x)
A function is even if f(-x) = f(x) and odd if f(-x) = -f(x)

Distance and Midpoint

The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be calculated using the formula ((x1 + x2)/2, (y1 + y2)/2)

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Review questions for the final exam of MAC 1105C, covering topics such as radical equations, quadratic equations, and functions. Test your knowledge and get ready for the exam!

MAC 1105C - Final Exam Review