The content, assignments, and assessments for Precalculus I are aligned to the following learning outcomes.

State Mandated Learning Objectives for MA 203 (corresponds to TCC’s MATH 1513)

1.    Identify quantities and changes in quantities in mathematical representations, and distinguish constants from variables.
2.    Compute and interpret constant and average rates of change of quantities in multiple representations.
3.    Create models for real-world situations through appropriate mathematical strategies.
4.    Interpret functions and convert between their representations, including symbols, tables, graphs, and words.
5.    Algebraically solve equations including linear, quadratic, polynomial, rational, radical, absolute value,
exponential, and logarithmic.
6.    Algebraically solve inequalities including linear, quadratic, polynomial, rational, and absolute value.
7.    Solve systems of linear and non-linear equations.
8.    Perform operations on functions and identify the properties and characteristics of functions. Such properties and characteristics include domain and range, increasing and decreasing, one-to-one, inverses, even and odd, end behavior, relative extrema, and vertical and horizontal asymptotes.
9.   Identify and sketch graphs of functions including linear, polynomial, absolute value, rational, radical, piecewise functions, exponential, logarithmic, and use transformations of basic graphs.

TCC Course Learning Outcomes for MATH 1513: (Critical Thinking CLOs 1 – 5)

Students will be able to:

1. Solve equations and inequalities. (Links to State Objectives 1, 3, 4, 5, & 6.)
2. Identify the properties of functions. (Links to State Objectives 1, 2, 4, 8, 9, & 11.)
3. Apply polynomial and rational theorems. (Links to State Objectives 3, 10, 11, & 12.)
4. Analyze exponential and logarithmic functions. (Links to State Objectives 3, 4, 5 10, 11, & 12.)
5. Solve systems of equations. (Links to State Objective 7.)

Unit 1: Graphs & Functions

• Determine whether a relation represents a function
• Find the value of a function
• Determine whether a function is one-to-one
• Use the vertical line test to identify functions
• Graph the functions listed in the library of functions
• Find the domain of a function defined by an equation
• Write Domain and Range Using Standard Notations
• Find Domain and Range from a Graph
• Define Domain and Range of Toolkit Functions
• Graph Piecewise-Defined Functions
• Find the average rate of change of a function
• Use a graph to determine where a function is increasing, decreasing, or constant
• Use a graph to locate local maxima and local minima
• Use a graph to locate the absolute maximum and absolute minimum
• Combine functions using algebraic operations
• Create a new function by composition of functions
• Evaluate composite functions
• Find the domain of a composite function
• Decompose a composite function into its component functions
• Graph functions using vertical and horizontal shifts
• Graph functions using reflections about the [latex]x[/latex] -axis and the [latex]y[/latex] -axis
• Determine whether a function is even, odd, or neither from its graph
• Graph functions using compressions and stretches
• Combine transformations
• Verify inverse functions
• Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
• Find or evaluate the inverse of a function
• Use the graph of a one-to-one function to graph its inverse function on the same axes
• Represent a linear function with an equation, words, a table and a graph
• Determine whether a linear function is increasing, decreasing, or constant.
• Write and interpret a linear function.

• Graph linear functions by plotting points, using the slope and y-intercept, and by using transformations
• Write the equation of a linear function given it’s graph, including vertical and horizontal lines, match linear equations with their graphs
• Find the equations of vertical and horizontal lines
• Graph an absolute value function, find it’s intercepts

• Identify steps for modeling and solving.
• Build linear models from verbal descriptions.
• Draw and interpret scatter plots.
• Find the line of best fit using an online graphing tool.
• Distinguish between linear and nonlinear relations.
• Use a linear model to make predictions.

Unit 2: Polynomial and Rational Functions

• Recognize characteristics of parabolas
• Understand how the graph of a parabola is related to its quadratic function
• Use the quadratic formula and factoring to find both real and complex roots (x-intercepts) of quadratic functions
• Use algebra to find the y-intercepts of a quadratic function
• Solve problems involving the roots and intercepts of a quadratic function
• Use the discriminant to determine the nature (real or complex) and quantity of solutions to quadratic equations
• Determine a quadratic function’s minimum or maximum value
• Solve problems involving a quadratic function’s minimum or maximum value
• Identify power functions.
• Identify end behavior of power functions.
• Identify polynomial functions.
• Identify the degree and leading coefficient of polynomial functions.
• Identify local behavior of polynomial functions.

• Identify zeros of polynomial functions with even and odd multiplicity
• Use the degree of a polynomial to determine the number of turning points of its graph
• Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem
• Write the equation of a polynomial function given it’s graph

• Use long division to divide polynomials.
• Use synthetic division to divide polynomials.
• Evaluate a polynomial using the Remainder Theorem.
• Use the Factor Theorem to solve a polynomial equation.
• Use the Rational Zero Theorem to find rational zeros.
• Find zeros of a polynomial function.
• Use the Linear Factorization Theorem to find polynomials with given zeros.
• Use Descartes’ Rule of Signs.
• Solve real-world applications of polynomial equations
• Use arrow notation to describe end behavior of rational functions
• Solve applied problems involving rational functions.
• Find the domains of rational functions.
• Identify vertical and horizontal asymptotes of graphs of rational functions
• Graph rational functions.
• Find the inverse of a polynomial function.
• Restrict the domain to find the inverse of a polynomial function.

Unit 3: Exponential and Logarithmic Functions

• Evaluate an exponential growth function with different bases
• Use a compound interest Formula
• Write an exponential function
• Find an exponential function given a graph
• Use a graphing calculator to find an exponential function
• Find an exponential function that models continuous growth or decay
• Graph exponential functions, determine whether a graph represents exponential growth or decay
• Graph exponential functions using transformations.
• Convert from logarithmic to exponential form.
• Convert from exponential to logarithmic form.
• Evaluate common and natural logarithms.
• Identify the domain of a logarithmic function.
• Graph logarithmic functions using transformations, and identify intercepts and the vertical asymptote
• Identify why and how a logarithmic function is an inverse of an exponential function
• Use power, product, and quotient rules to expand and condense logarithms
• Use the change-of-base formula for logarithms.
• Use like bases to solve exponential equations.
• Use logarithms to solve exponential equations.
• Use the definition of a logarithm to solve logarithmic equations.
• Use the one-to-one property of logarithms to solve logarithmic equations.
• Solve applied problems involving exponential and logarithmic equations.
• Model exponential growth and decay.
• Use Newton’s Law of Cooling.
• Use logistic-growth models.
• Choose an appropriate model for data.
• Express an exponential model in base e.
• Build an exponential model from data.

Unit 4: Systems, Matrices, Conic Sections, Sequences & Series

• Solve systems of equations by graphing, substitution, and addition.
• Identify inconsistent systems of equations containing two variables.
• Express the solution of a system of dependent equations containing two variables using standard notations.
• Solve a system of nonlinear equations using substitution or elimination.
• Graph a nonlinear inequality.
• Graph a system of nonlinear inequalities.
• Solve systems of three equations in three variables.
• Identify inconsistent systems of equations containing three variables.
• Express the solution of a system of dependent equations containing three variables using standard notations.
• Find the sum and difference of two matrices.
• Find scalar multiples of a matrix.
• Find the product of two matrices.
• Write the augmented matrix of a system of equations.
• Write the system of equations from an augmented matrix.
• Perform row operations on a matrix.
• Solve a system of linear equations using matrices.
• Find the inverse of a matrix.
• Solve a system of linear equations using an inverse matrix.
• Write equations of ellipses in standard form
• Graph ellipses centered at the origin
• Graph ellipses not centered at the origin
• Solve applied problems involving ellipses
• Locate a hyperbola’s vertices and foci
• Write equations of hyperbolas in standard form
• Graph hyperbolas centered at the origin
• Graph hyperbolas not centered at the origin
• Solve applied problems involving hyperbolas
• Graph parabolas with vertices at the origin
• Write equations of parabolas in standard form
• Graph parabolas with vertices not at the origin
• Solve applied problems involving parabolas

Additional Assignments

• Write the terms of a sequence defined by an explicit formula
• Write the terms of a sequence defined by a recursive formula
• Use factorial notation
• Find the common difference for an arithmetic sequence
• Write terms of an arithmetic sequence
• Use a recursive formula for an arithmetic sequence
• Use an explicit formula for an arithmetic sequence
• Find the common ratio for a geometric sequence
• List the terms of a geometric sequence
• Use a recursive formula for a geometric sequence
• Use an explicit formula for a geometric sequence
• Use summation notation
• Use the formula for the sum of the first [latex]n[/latex] terms of an arithmetic series
• Use the formula for the sum of the first [latex]n[/latex] terms of a geometric series
• Use the formula for the sum of an infinite geometric series
• Solve annuity problems