High School Functions (Wisconsin Standards)

Interpreting Functions (F.IF)

• M.F.IF.A.1 Understand a function as assigning each domain element exactly one range element, with f(x) as the output.
• M.F.IF.A.2 Use and evaluate function notation and interpret it in context.
• M.F.IF.A.3 Recognize sequences as functions on integer domains, sometimes defined recursively.
• M.F.IF.B.4 Interpret key features of graphs and tables in context and sketch graphs from descriptions.
• M.F.IF.B.5 Relate a function's domain to its graph and choose a suitable discrete or continuous domain.
• M.F.IF.B.6 Calculate and interpret average rate of change over an interval and estimate it from a graph.
• M.F.IF.C.7 Graph functions from symbols and show key features efficiently.
  • a. Graph linear, quadratic and exponential functions.
  • b. Graph square root, cube root, piecewise and absolute value functions.
  • c. Graph polynomials, showing zeros and end behavior.
  • d. Graph rational functions, showing zeros and asymptotes.
  • e. Graph logarithmic and trig functions with key features.
• M.F.IF.C.8 Rewrite a function in equivalent forms to reveal and explain its properties.
  • a. Rewrite quadratics in vertex or factored form and interpret.
  • b. Use exponent properties to find percent rates of change.
• M.F.IF.C.9 Compare properties of two functions represented in different ways.

Building Functions (F.BF)

• M.F.BF.A.1 Write a function for a relationship between two quantities.
  • a. Find an explicit expression, recursive process or steps from context.
  • b. Combine standard functions with arithmetic operations.
  • c. Compose functions using tables, graphs and symbols.
• M.F.BF.A.2 Write arithmetic and geometric sequences recursively and explicitly and translate between forms.
• M.F.BF.B.3 Identify how f(x) + k, kf(x), f(kx) and f(x + k) change a graph and find k from graphs.
• M.F.BF.B.4 Find and build inverse functions with tables, graphs and algebra.
• M.F.BF.B.5 Understand exponents and logarithms as inverses and use this to solve problems.

Linear, Quadratic, and Exponential Models (F.LE)

• M.F.LE.A.1 Tell situations modeled by linear functions from those modeled by exponential functions.
  • a. Prove linear grows by equal differences, exponential by equal factors.
  • b. Recognize a constant rate of change.
  • c. Recognize a constant percent rate of change.
• M.F.LE.A.2 Build linear and exponential functions, including sequences, from graphs, descriptions or input–output pairs.
• M.F.LE.A.3 Observe with graphs and tables that exponential growth eventually exceeds linear or polynomial growth.
• M.F.LE.A.4 Write solutions of exponential equations as logarithms (base 2, 10 or e) and evaluate with technology.
• M.F.LE.B.5 Interpret the parameters of a linear or exponential function in context.

Trigonometric Functions (F.TF)

• M.F.TF.A.1 Understand radian measure as arc length on the unit circle.
• M.F.TF.A.2 Explain how the unit circle extends trig functions to all real numbers.
• M.F.TF.A.3 Use special triangles for exact trig values at π/3, π/4 and π/6 and the unit circle for related angles.
• M.F.TF.A.4 Use the unit circle to explain symmetry and periodicity of trig functions.
• M.F.TF.B.5 Choose trig functions to model periodic situations with given amplitude, frequency and midline.
• M.F.TF.B.6 Understand that restricting a trig function's domain allows its inverse to be defined.
• M.F.TF.B.7 Use inverse trig functions to solve equations from modeling and interpret the solutions.
• M.F.TF.C.8 Prove sin²θ + cos²θ = 1 and use it to find trig values given the quadrant.
• M.F.TF.C.9 Prove the sum and difference formulas for sine, cosine and tangent and apply them.