Jump Start to Precalculus is a four-week intensive course designed to equip students with the essential algebraic skills and foundational concepts necessary for success in precalculus and calculus. Through a blend of review and introduction to new topics, students will gain confidence in graphing, equation solving, and function manipulation—preparing them for the challenges of higher-level mathematics.

Linear Equations and Graphing

• Master the art of writing equations of lines from various forms, including standard form
• Graph linear equations efficiently using intercepts—a crucial skill for calculus
• Recognize and graph vertical lines—understanding their unique properties

Absolute Value Equations and Inequalities

• Solve absolute value equations by isolating the absolute value expression
• Understand the dual-case nature of absolute value problems—considering both positive and negative scenarios
• Identify absolute value equations with no solutions—recognizing inherent contradictions
• Extend techniques to solving more complex absolute value equations with variables on both sides

Transformations of Functions

• Explore horizontal and vertical shifts—understanding their impact on function graphs
• Apply horizontal and vertical stretches and compressions—manipulating function shape
• Grasp the inverse relationship between transformations inside the function and their effect on the graph
• Connect transformations to various function families—linear, quadratic, absolute value, etc.

Imaginary and Complex Numbers

• Define imaginary numbers and their relationship to the square root of negative one
• Simplify powers of i—reducing them to one of four possible values
• Grasp the concept of complex numbers to represent situations where parabolas do not intersect the x-axis
• Perform operations on complex numbers—addition, subtraction, multiplication, and division

Factoring Techniques

• Apply various factoring methods—including difference of squares, perfect square trinomials, and grouping
• Factor higher-degree polynomials—preparing for advanced algebraic manipulations
• Utilize factoring to simplify complex expressions—a crucial skill for calculus
• Connect factoring to finding roots of polynomial functions

Functions and Their Properties

• Define function notation and its implications—understanding inputs and outputs
• Evaluate functions for given inputs—a fundamental skill in mathematical analysis
• Determine the domain and range of various functions—identifying valid input and output values
• Analyze function behavior—including increasing/decreasing intervals, intercepts, and symmetry

Inverse Functions

• Understand the concept of inverse functions—reversing the roles of input and output
• Verify inverse functions—using composition to confirm their relationship
• Determine when a function has an inverse—understanding the horizontal line test
• Find the inverse of a function algebraically—swapping x and y and solving