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
Search for Sections 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:
 Determine domain, range, intercepts, and graph a function by plotting points.
 Determine if a relation is a function.
 Demonstrate a working knowledge of function notation and terminology.
 Perform operations on functions including the difference quotient.
 Demonstrate a working knowledge of the features of the graph of a function.
 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.
 Graph piecewisedefined 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:
 Recognize polynomial and rational functions and determine domain and range of these functions.
 Graph quadratic functions using its vertex, intercepts, and axis of symmetry.
 Graph power functions using transformations.
 Graph and analyze higher order polynomial functions (use end behavior, zeros, and sign tests).
 Find all zeros using Rational Roots Theorem and division of polynomials.
 Use quadratic and polynomial functions in various applications.
 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:
 Demonstrate a working knowledge of the definition of an exponential function.
 Demonstrate a working knowledge of the definition of a logarithm, including the fact that logarithmic and exponential functions are inverses.
 Use the laws of exponents and properties of logarithms to simplify or evaluate expressions.
 Graph exponential and logarithmic functions using transformations.
 Determine domain and range of exponential and logarithmic functions.
 Use the numbers 10 and e as bases for exponential and logarithmic functions, including use of ChangeofBase Formula
 Use properties of logarithms to expand and condense logarithmic expressions.
 Solve exponential and logarithmic equations.
 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:
 Find the center and radius of a circle from its equation and graph.
 Find the vertex, focus, and directrix of a parabola from its equation and graph.
 Identify key features of the ellipse and hyperbola including the center, foci, vertices, and asymptotes from their equations and graph.
 Convert equations of conic sections from general form to standard form.
 Identify a conic section from its equation.
 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
 Review of Fundamentals of Algebra
 Linear and nonlinear equations and inequalities
 Absolute value equations and inequalities
 Radical equations
 Equations and graphs of lines
 Functions
 Evaluate a function
 Sum, difference, product, quotient, and composition of two functions
 Difference quotient
 The graph of a function
 Vertical Line Test
 Domain, range, and intercepts
 Symmetry
 Even and odd
 Increasing, decreasing, and constant
 Local and absolute extrema
 Evaluate and graph piecewisedefined functions
 Graph functions using transformations
 Vertical and horizontal shifting
 Reflection
 Stretching and compressing
 Polynomial and Rational Functions
 Quadratic functions
 Graph using vertex, axis of symmetry, and intercepts
 Maximum and minimum value
 Quadratic models and optimization
 Graph power functions using transformations
 Zeros of a polynomial function
 Remainder, factor, and rational root theorems
 Division of polynomials including synthetic division
 Fundamental Theorem of Algebra
 Complex zeros and conjugate pairs
 Graph higherdegree polynomial functions
 End behavior (Leading Term Test)
 Zeros and their multiplicity
 Sign tests
 Graph rational functions
 Domain
 Vertical and horizontal asymptotes (optional: slant asymptotes)
 Graph y = 1/x and y = 1/x^2 using transformations, intercepts, and asymptotes
 Graph other rational functions using intercepts, symmetry, asymptotes, and sign tests
 Exponential and Logarithmic Functions
 Onetoone and inverse functions
 Evaluate exponential functions including base 10 and e
 Evaluate logarithmic expressions including base 10 and e
 Graph exponential and logarithmic functions using domain, intercepts, asymptotes, and transformations
 Properties of logarithms including product property, quotient property, power property, and changeofbase formula
 Solve exponential and logarithmic equations
 Financial and exponential growth and decay models
 Conic Sections
 Graph from standard form of the equation with center/vertex at (h,k)
 Circle  use center and radius
 Parabola  use vertex, focus, and directrix
 Ellipse  use center, vertices, and foci
 Hyperbola  use center, vertices, foci, and asymptotes
 Find an equation from the graph
 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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