MATH& 141 Precalculus I • 5 Cr.
Emphasizes graphs and polynomial functions. Other topics include the theory of equations and rational, exponential, inverse, and logarithmic functions. Either MATH& 141 or MATH 138 may be taken for credit, not both. Fulfills the quantitative or symbolic reasoning course requirement at BC. Prerequisite: Placement by assessment or MATH 099 with a B- or better.
After completing this class, students should be able to:
- Demonstrate knowledge of College Algebra from and Elementary Functions approach in preparation for Calculus I, II, and III.
- Build and demonstrate knowledge of using a graphing calculator and utilizing it as an aid in understanding as well as solving College Algebra and Pre-calculus concepts and exercises.
- Solve 1st degree inequalities including double inequalities and absolute value inequalities. Solve 1srt degree and 2nd degree and rational equations including Quadratic formula and apply it to solving 2nd degree and 3rd degree and rational inequalities using the Test Value Method. Solve related inequality application and to interpret the solutions and make inferences.
- Demonstrate knowledge of Rectangular Coordinate System graphing by plotting. Apply Distance and Midpoint Formulas into learning of the equations for circles. Identify symmetry in a graph and recognize its associated advantages and limitations.
- Graph straight lines with slope formula, slope-intercept formula, point-slope formula, and perpendicular slope formula and apply these in analyzing and solving applications related to straight lines.
- Recognize functions in symbolic, graphical, and tabular formats. Identify Domain and Range in each of these formats. Use Functional Notation and evaluation leading to sketching functions. Identify graphs as decreasing or increasing. Build functions to describe various Application Problems and interpret the results and make inferences.
- Graph functions in general including utilizing the properties of shifting, stretching, and reflecting and recognize its advantages over point. Given the initial and the final graphs describe symbolically which effect were used. Use a graphing calculator to identify these general properties easier. Identify and contrast Even and Odd functions, as well as Piece-Wise defined functions including the Greatest Integer Function.
- Recognize 2nd degree or Quadratic Functions and their associated Parabolic Graphs. Find the Vertex from the Vertex Form and/or by Formula and apply it in graphing Parabolas. Use the Quadratic Formula to find the zeros of a Quadratic Function.
- Combine functions utilizing operations of Addition, Subtraction, Multiplication, Division, and Composition and find the new Domain for each, with the functions being given symbolically, graphically or by a table. Solve related Applications using the Composition Operations.
- Identify Inverse Functions and One to One functions. Verify two functions are inverses by using composition. Find Inverse Functions given the original function symbolically or graphically or by table.
- Analyze and Graph Polynomials of Nth degree utilizing general properties of Polynomials and locate the zeros and find and plot test points between and beyond the zeros. Solve related Application Problems and to interpret the solutions.
- Identify Complex numbers and Add, Subtract, Multiply, and divide. Find and describe complex roots using conjugates after factoring or using the Quadratic Formula.
- Divide Polynomials, and show knowledge of Synthetic Division. Recognize the connection between Synthetic division and the Reminder and Factor Theorems.
- Apply the Theory of Equations including the Fundamental Theorem of Algebra, factored form of polynomials, multiplicity of zeros, and bounds on real zeros to graph polynomials and compare and contrast different polynomial graphs.
- Recognize the Complex roots come in pairs. Find Rational zeros using the Rational Roots Theorem and to reduce to the Quadratic level for future solving. Solve related Application Problems and to interpret the solutions.
- Analyze and graph Rational Functions through a multi-step process including finding all Intercepts, Domain, all Asymptotes, and plotting a couple of relevant test points. Identify and find Vertical, Horizontal, and Slant Asymptotes. Solve related Application Problems and to interpret the solutions and make inferences.
- Analyze and graph Exponential and Logarithmic functions. Solve related Applications and to interpret the solutions. Identify the Natural Exponential and the Natural Logarithm Functions with base “e”, and utilize them to solve and interpret solutions to Compounded Interest and Continuously Compounded Interest Applications as well as making inferences in Population, Radioactive Decay, Drug level and other applications.