PreCalculus

Analyze functions and relations.

• PC.F.1.1(Objective)

  Interpret characteristics of a function defined by an expression in the context of the situation.

• PC.F.1.2(Objective)

  Sketch the graph of a function that models a relationship between two quantities, identifying key features.

• PC.F.1.3(Objective)

  Interpret characteristics of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.

• PC.F.1.4(Objective)

  Describe end behavior, asymptotic behavior, and points of discontinuity.

• PC.F.1.5(Objective)

  Determine if a function has an inverse. Algebraically and graphically find the inverse or define any restrictions on the domain that meet the requirement for invertibility, and find the inverse on the restricted domain.

Build functions to model and validate relationships among functions.

• PC.F.2.1(Objective)

  Model relationships through composition, and attend to the restrictions of the domain.

• PC.F.2.2(Objective)

  Rewrite a function as a composition of functions.

• PC.F.2.3(Objective)

  Interpret the meanings of quantities involving functions and their inverses.

• PC.F.2.4(Objective)

  Verify by analytical methods that one function is the inverse of another.

Predict and verify solutions involving functions.

• PC.F.3.1(Objective)

  Predict solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.

• PC.F.3.2(Objective)

  Graphically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.

• PC.F.3.3(Objective)

  Algebraically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.

Investigate conic sections.

• PC.CS.1.1(Objective)

  Model real-world situations which involve conic sections.

• PC.CS.1.2(Objective)

  Identify key features of conic sections (foci, directrix, radii, axes, asymptotes, center) graphically and algebraically.

• PC.CS.1.3(Objective)

  Sketch a graph of a conic section using its key features.

• PC.CS.1.4(Objective)

  Write the equation of a conic section given its key features.

• PC.CS.1.5(Objective)

  Given the equation 𝑎𝑥² + 𝑏𝑦² + 𝑐𝑥 + 𝑑𝑦 + 𝑒 = 0, determine if the equation represents a circle, ellipse, parabola, or hyperbola.

Make sense of the unit circle and its relationship to the graphs of trigonometric functions.

• PC.T.1.1(Objective)

  Draw and recognize angles in standard position using radian measure, and determine the quadrant of the terminal side.

• PC.T.1.2(Objective)

  Convert radian measure to degree measure and vice-versa.

• PC.T.1.3(Objective)

  Find the length of an arc and the area of a sector on a circle.

• PC.T.1.4(Objective)

  Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for 𝜋 − 𝑥, 𝜋 + 𝑥, and 2𝜋 − 𝑥 in terms of their values for x, where x is any real number.

• PC.T.1.5(Objective)

  Use reference angles to determine the terminal point P(x, y) on the unit circle for a given angle.

• PC.T.1.6(Objective)

  Estimate trigonometric values of any angle.

• PC.T.1.7(Objective)

  Apply the properties of a unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

• PC.T.1.8(Objective)

  Graph all six trigonometric functions, identifying key features.

• PC.T.1.9(Objective)

  Describe and analyze the relationships of the properties of a unit circle.

Apply trigonometric concepts beyond the right triangle.

• PC.T.2.1(Objective)

  Create models for situations involving trigonometry.

• PC.T.2.2(Objective)

  Apply the Law of Sines and Law of Cosines to solve problems.