AP Precalculus 1.1 to 2.14

AP Precalculus - 1.1 to 2.14

• 1.1 - Functions and Function Notation:

  • A function is a relation where each input (domain) is associated with exactly one output (range).
  • Function notation (f(x)) shows the output of a function (f) for a given input (x).
  • Identify functions from graphs, tables, and equations.

• 1.2 - Linear Functions:

  • Linear functions have a constant rate of change, graphing as straight lines.
  • Slope-intercept form: y = mx + b (where m is the slope, b the y-intercept).
  • Point-slope form: y - y₁ = m(x - x₁)
  • Find a line's equation given two points or a point and slope.
  • Understand parallel and perpendicular lines.

• 1.3 - Transformations of Functions:

  • Transformations include shifts (vertical, horizontal), reflections (x-axis, y-axis), stretches/compressions (vertical, horizontal).
  • Transformations affect the graph of a function.
  • Combine transformations to describe a function's graph.

• 1.4 - Quadratic Functions:

  • Quadratic functions are in the form f(x) = ax² + bx + c (where a, b, and c are constants, and a ≠ 0).
  • Quadratic graphs are parabolas.
  • Find the vertex, x-intercepts, and y-intercept of a parabola.
  • Understand standard and vertex forms of a quadratic equation.
  • Solve quadratic equations by factoring, completing the square, and using the quadratic formula.

• 1.5 - Polynomial Functions:

  • Polynomial functions are in the form f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ +...+ a₁x + a₀ .
  • Understand degree, leading coefficient, and end behavior of polynomial graphs.
  • Find zeros and factors of a polynomial.

• 1.6 - Rational Functions:

  • Rational functions are the quotient of two polynomial functions (often in the form f(x) = p(x)/q(x)).
  • Identify vertical, horizontal, and oblique asymptotes in rational functions.
  • Analyze rational function behavior at asymptotes and key points.

• 1.7 - Exponential and Logarithmic Functions:

  • Exponential functions are in the form f(x) = a^x (where a > 0 and a ≠ 1).
  • Logarithmic functions are the inverses of exponential functions.
  • Understand properties of logarithms and exponents.
  • Apply exponential growth/decay models.
  • Understand the natural base e in exponential growth/decay.

• 1.8 - Inverse Functions:

  • Inverse functions reverse each other (f(f⁻¹(x)) = x and f⁻¹(f(x)) = x).
  • Find the inverse of a function algebraically and graphically.
  • Determine if a function has an inverse.

• 1.9 - Trigonometric Functions:

  • Understand the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) and their unit circle relationships.
  • Apply trigonometric identities and their uses.
  • Evaluate trigonometric functions for various angles.
  • Graph trigonometric functions.

• 1.10 - Trigonometric Identities and Equations:

  • Prove and use fundamental trigonometric identities (e.g., Pythagorean identities).
  • Solve trigonometric equations.

• 1.11 - Trigonometric Graphs:

  • Graph various trigonometric functions, including transformations.

• 2.1-2.14 (Sections of Chapter 2):

  • These sections likely expand on chapter 1 topics.
  • More advanced applications, graphs, equations, problem-solving, and mathematical modeling are likely included.
  • Specific topics depend on the content of chapter 2.