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# MATH 1415 - Precalculus I: College Algebra

Credit Hours: 4.00

Prerequisites: MATH 1050  or MATH 1050X  with grade C or better; or an equivalent college course; or an acceptable score on a placement or prerequisite exam

(formerly MATH 1410)

No credit after MATH 1410, MATH 1420, MATH 1450, MATH 1460, or MATH 1465. MATH 1415 is the first of two courses whose combined content with MATH 1435 parallels that of MATH 1465. Topics include functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, and conics.

Billable Contact Hours: 4

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Transfer Possibilities
Michigan Transfer Network (MiTransfer) - Utilize this website to easily search how your credits transfer to colleges and universities.
OUTCOMES AND OBJECTIVES
Outcome 1: Upon completion of this course, students will be able to demonstrate a working knowledge of fundamental concepts of functions.

Objectives: The student will:

1. Determine domain, range, intercepts, and graph a function by plotting points.
2. Determine if a relation is a function.
3. Demonstrate a working knowledge of function notation and terminology.
4. Perform operations on functions including the difference quotient.
5. Demonstrate a working knowledge of the features of the graph of a function.
6. Graph functions using transformations. The functions used should include: x^2, x^3, |x|, 1/x, 1/x^2, square root of x, cube root of x. Use asymptotes to help graph f(x) = 1/x, g(x) = 1/x^2, and their transformations.
7. Graph piecewise-defined functions.

Outcome 2: Upon completion of this course, students will be able to demonstrate a working knowledge of polynomial and rational functions.

Objectives: The student will:

1. Recognize polynomial and rational functions and determine domain and range of these functions.
2. Graph quadratic functions using its vertex, intercepts, and axis of symmetry.
3. Graph power functions using transformations.
4. Graph and analyze higher order polynomial functions (use end behavior, zeros, and sign tests).
5. Find all zeros using Rational Roots Theorem and division of polynomials.
6. Use quadratic and polynomial functions in various applications.
7. Graph rational functions using asymptotes, zeros, and sign tests.

Outcome 3: Upon completion of this course, students will be able to demonstrate a working knowledge of exponential and logarithmic functions.

Objectives: The student will:

1. Demonstrate a working knowledge of the definition of an exponential function.
2. Demonstrate a working knowledge of the definition of a logarithm, including the fact that logarithmic and exponential functions are inverses.
3. Use the laws of exponents and properties of logarithms to simplify or evaluate expressions.
4. Graph exponential and logarithmic functions using transformations.
5. Determine domain and range of exponential and logarithmic functions.
6. Use the numbers 10 and e as bases for exponential and logarithmic functions, including use of Change-of-Base Formula
7. Use properties of logarithms to expand and condense logarithmic expressions.
8. Solve exponential and logarithmic equations.
9. Solve applications such as exponential growth/decay and other applications in physical science.

Outcome 4: Upon completion of this course, students will be able to demonstrate a working knowledge of the equations and graphs of conic sections.

Objectives: The student will:

1. Find the center and radius of a circle from its equation and graph.
2. Find the vertex, focus, and directrix of a parabola from its equation and graph.
3. Identify key features of the ellipse and hyperbola including the center, foci, vertices, and asymptotes from their equations and graph.
4. Convert equations of conic sections from general form to standard form.
5. Identify a conic section from its equation.
6. Find an equation of a conic section from its graph.

COMMON DEGREE OUTCOMES (CDO)
• Communication: The graduate can communicate effectively for the intended purpose and audience.
• Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue.
• Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives.
• Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task.
• Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments.
• Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course:
Critical Thinking: YES
Quantitative Reasoning: YES
COURSE CONTENT OUTLINE

1. Review of Fundamentals of Algebra
1. Linear and nonlinear equations and inequalities
2. Absolute value equations and inequalities
4. Equations and graphs of lines
2. Functions
1. Evaluate a function
2. Sum, difference, product, quotient, and composition of two functions
3. Difference quotient
4. The graph of a function
1. Vertical Line Test
2. Domain, range, and intercepts
3. Symmetry
4. Even and odd
5. Increasing, decreasing, and constant
6. Local and absolute extrema
5. Evaluate and graph piecewise-defined functions
6. Graph functions using transformations
1. Vertical and horizontal shifting
2. Reflection
3. Stretching and compressing
3. Polynomial and Rational Functions
1. Graph using vertex, axis of symmetry, and intercepts
2. Maximum and minimum value
2. Graph power functions using transformations
3. Zeros of a polynomial function
1. Remainder, factor, and rational root theorems
2. Division of polynomials including synthetic division
3. Fundamental Theorem of Algebra
4. Complex zeros and conjugate pairs
4. Graph higher-degree polynomial functions
1. End behavior (Leading Term Test)
2. Zeros and their multiplicity
3. Sign tests
5. Graph rational functions
1. Domain
2. Vertical and horizontal asymptotes (optional: slant asymptotes)
3. Graph y = 1/x and y = 1/x^2 using transformations, intercepts, and asymptotes
4. Graph other rational functions using intercepts, symmetry, asymptotes, and sign tests
4. Exponential and Logarithmic Functions
1. One-to-one and inverse functions
2. Evaluate exponential functions including base 10 and e
3. Evaluate logarithmic expressions including base 10 and e
4. Graph exponential and logarithmic functions using domain, intercepts, asymptotes, and transformations
5. Properties of logarithms including product property, quotient property, power property, and change-of-base formula
6. Solve exponential and logarithmic equations
7. Financial and exponential growth and decay models
5. Conic Sections
1. Graph from standard form of the equation with center/vertex at (h,k)
1. Circle - use center and radius
2. Parabola - use vertex, focus, and directrix
3. Ellipse - use center, vertices, and foci
4. Hyperbola - use center, vertices, foci, and asymptotes
2. Find an equation from the graph
3. Write the standard form of the equation from the general form by completing the square

Primary Faculty
Miller, Faith
Secondary Faculty
Donnelly, Christopher
Associate Dean
McMillen, Lisa
Dean
Pritchett, Marie

Primary Syllabus - Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088

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