Functions

AIII.F.23Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.AIII.F.24Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.AIII.F.25Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.AIII.F.26Verify by composition that one function is the inverse of another.AIII.F.27Read values of an inverse function from a graph or a table, given that the function has an inverse.AIII.F.28Produce an invertible function from a non-invertible function by restricting the domain.AIII.F.29Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.AIII.F.30Use 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.AIII.F.31Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.AIII.F.32Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.AIII.F.33Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.AIII.F.34Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.AIII.F.35Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.AIII.F.36Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
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