# MAT 129 - Precalculus **Credits:** **5**
**Lecture Hours:** **5**
**Lab Hours:** **0**
**Practicum Hours:** **0**
**Work Experience:** **0**
**Course Type:** **Core** Polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, vectors, complex numbers, elementary theory of equations, linear systems, matrices, and analytic geometry.
*Prerequisite:* Minimum ALEKS scores of 61% or MAT 130 with a C- or better
**Competencies**
- Analyze mathematical functions
- Define a function
- Determine if a relation is a function
- Find the domain and range of a function
- Determine minimum and maximum values of a function
- Determine whether functions are increasing, decreasing or constant
- Determine whether functions have even or odd properties
- Graph functions
- Identify common functions
- Identify transformations
- Combine functions using addition, subtraction, multiplication, or division
- Define an inverse function
- Find inverse function
- Use polynomial functions
- Define a polynomial function
- Determine the standard form of a quadratic function
- Determine the vertex and any x-intercepts of a quadratic function
- Find zeros of a polynomial function
- State the fundamental Theorem of Algebra
- apply the intermediate value, remainder, factor, and rational root theorems to find polynomial roots
- Identify rational functions
- Define a rational function
- Identify any horizontal and vertical asymptotes
- Graph a rational function
- Use exponential functions
- Define exponential functions
- Graph exponential functions
- Solve exponential equations
- Use logarithmic functions
- Define logarithmic functions
- Apply the properties of logarithms
- Graph logarithmic functions
- Solve logarithmic equations
- Apply exponential and logarithmic functions to problems involving interest, growth and decay
- Use trigonometric functions for oblique triangles
- Apply the Law of Sines and Law of Cosines
- Find the area of SAS triangles
- Find the area of SSS triangles using heron’s formula
- Use vectors in the plane
- Perform scalar multiplication and vector addition
- Find the dot product of two vectors
- Apply properties of the dot product
- Find the angle between two vectors
- Find vector components using projection of one vector onto another
- Use the trigonometric form of complex numbers
- Find the trigonometric form of a complex number
- Find the modulus of a complex number
- Multiply and divide complex numbers
- Find powers and roots of complex numbers
- Solve systems of equations
- Use the substitution and elimination methods to solve a system of equations
- Identify whether a system of equations has zero, one, or infinitely many solutions
- Use row-echelon form and back-substitution to solve a system of equations
- Solve nonsquare systems of equations using a parameter
- Decompose a fraction into partial fraction equivalents
- Use matrices
- Use Gaussian Elimination with back-substitution to solve a system of equations using row operations on matrices
- Use Gauss-Jordan Elimination to solve a system of equations
- Perform the operations of matrix addition, scalar multiplication, and matrix multiplication
- Determine the inverse of a nonsingular matrix
- Solve a system of equations using the inverse matrix
- Find the determinant of a square matrix
- Use Cramer’s Rule to solve a linear system of equations
- Analyze conic sections using rectangular coordinates
- Find the standard equation of a parabola, an ellipse, and a hyperbola
- Find the vertex, focus, and directrix of a parabola
- Find the center, vertices, foci, and eccentricity of an ellipse
- Find the center, vertices, foci, and asymptotes of a hyperbola
- Classify a conic from its general equation
- Analyze conic sections using polar coordinates
- Convert coordinates and equations from rectangular to polar and vice versa
- Graph polar equations by testing for symmetry
- Identify and graph a conic by examining the polar form of the equation
- Graph points, lines, vectors and surfaces in space
- Plot points, find distances between points, and find midpoints of segments
- Write equations of spheres
- Find dot products of vectors and angles between vectors
- Find cross products of vectors
- Find limits
- Use properties and operations of limits
- Find limits by direct substitution, dividing out, and rationalizing
- Find slopes by use of tangents lines, the limit definition of slope, and derivatives
- Find limits at infinity and limits of sequences
- Find limits of summations
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