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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
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Polynomials Intro
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Multiplying Polynomials
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Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
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Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
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The Square Root Property
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Completing the Square
(0)

The Quadratic Formula
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Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
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Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
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Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
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The Number e
(0)

Introduction to Logarithms
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Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
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Coterminal Angles
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Complementary and Supplementary Angles
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Radians
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8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
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Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
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Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

6. Exponential and Logarithmic Functions

Introduction to Exponential Functions

6. Exponential and Logarithmic Functions

Introduction to Exponential Functions: Videos & Practice Problems

Video Lessons Practice Worksheet

20 problems

Problem 1Multiple Choice

If you have \$18,000 to deposit, which will give you larger return after 5 years: 0.84% compounded quarterly or 0.81% compounded continuously?

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Problem 2Multiple Choice

Use the compound interest formula A = P(1 + r/n)^nt to solve the problem. If \$8000 is deposited to an account with an interest rate of 1.18% compounded quarterly, what is its value after 10 years?

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Problem 3Multiple Choice

Consider the functions f(x) = e^x and g(x) = 4e^x/2. Apply transformations on the graph of f in constructing the graph of g. Graph the asymptotes and identify their equations. Then, use the graph to determine the domain and range of both functions.

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Problem 4Multiple Choice

Plot the given function on the rectangular coordinate system.
f(x) = (7/8)^x

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Problem 5Multiple Choice

Provide the domain and range of the function by graphing it.
f(x) = 11^{x +3} +27

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Problem 6Multiple Choice

Provide the domain and range of the function by graphing it.
f(x) = -(1/11)^x-7 +5

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Problem 7Multiple Choice

Solve for x in the given equation.

(1/e)^-3x = (1/e³)^2x+5

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Problem 8Multiple Choice

Graph f(x) = 5^x to start. After that, graph the provided function using transformations of this graph. Graph the asymptotes and provide equations. Find the function's domain and range using the graphs.
g(x) = 5^{x +3}

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Problem 9Multiple Choice

Which of the following is a condition for the base of an exponential function?

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Problem 10Multiple Choice

Is the function f(x) = 5^x an exponential function?

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Problem 11Multiple Choice

Evaluate the function f(x) = 3^x for x = 2.

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Problem 12Multiple Choice

What is the value of f(x) = 4^(-2)?