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US-MS

Math

Mississippi Math

Algebra III: Functions

Analyze functions using different representations

AIII.F.23

Partially covered
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

AIII.F.24

Fully covered
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

Build a function that models a relationship between two quantities

AIII.F.25

Mostly covered
Compose 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.

Build new functions from existing functions

AIII.F.26

Fully covered
Verify by composition that one function is the inverse of another.

AIII.F.27

Fully covered
Read values of an inverse function from a graph or a table, given that the function has an inverse.

AIII.F.28

Fully covered
Produce an invertible function from a non-invertible function by restricting the domain.

AIII.F.29

Fully covered
Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Extend the domain of trigonometric functions using the unit circle

AIII.F.30

Mostly covered
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.

AIII.F.31

Fully covered
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Model periodic phenomena with trigonometric functions

AIII.F.32

Fully covered
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

AIII.F.33

Mostly covered
Understand 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.34

Mostly covered
Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

Prove and apply trigonometric identities

AIII.F.35

Fully covered
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

AIII.F.36

Fully covered
Prove 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.