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

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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 (A) Signup and view all the answers

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

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

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

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

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

6/5 (A) Signup and view all the answers

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

{-1, 7} (C) 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 (D) Signup and view all the answers

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

No symmetry (D) 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) (C) 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 (D) Signup and view all the answers

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

Graph C (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) (B) Signup and view all the answers

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

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

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

e^2 (C) 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) (D) Signup and view all the answers

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

4 + 2log3x (C) 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) (C) 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 (B) Signup and view all the answers

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

an exponential decay (C) 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 (A) Signup and view all the answers

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

y = 3 (C) 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 (D) 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)} (B) Signup and view all the answers

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

√41 (D) 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 (D) 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 (C) 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 (A) Signup and view all the answers

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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)

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MAC 1105C - Final Exam Review

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