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STANDARDS

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Math

Mississippi Math

Algebra III: Algebra

Analyze and manipulate functions

AIII.A.8

Partially covered
Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).

AIII.A.9

Not covered
Determine the end behavior of polynomial functions.
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Use polynomial identities to solve problems

AIII.A.10

Fully covered
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

AIII.A.11

Fully covered
Verify the Binomial Theorem by mathematical induction or by a combinatorial argument.

AIII.A.12

Fully covered
Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

AIII.A.13

Fully covered
Write rational expressions in simplest form. (For example (x^3 – x^2 – x + 1)/(x^3 + x^2 – x – 1) = (x – 1)/(x + 1).

AIII.A.14

Not covered
Decompose a rational function into partial fractions.
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AIII.A.15

Not covered
Determine asymptotes and holes of rational functions, explain how each was found, and relate these behaviors to continuity.
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Perform operations on expressions, equations, inequalities and polynomials

AIII.A.16

Fully covered
Add, subtract, multiply and divide rational expressions.

AIII.A.17

Not covered
Solve polynomial and rational inequalities. Relate results to the behavior of the graphs.
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AIII.A.18

Fully covered
Find the composite of two given functions and find the inverse of a given function. Extend this concept to discuss the identity function f(x) = x.

AIII.A.19

Not covered
Simplify complex algebraic fractions (with/without variable expressions and integer exponents) to include expressing (f(x+h)-f(x))/h as a single simplified fraction when f(x) = 1/1-x for example.
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AIII.A.20

Not covered
Find the possible rational roots using the Rational Root Theorem.
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AIII.A.21

Mostly covered
Find the zeros of polynomial functions by synthetic division and the Factor Theorem.

AIII.A.22

Not covered
Graph and solve quadratic inequalities.
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