Perform arithmetic operations with complex numbers.

Use complex numbers in polynomial identities and equations.

Polynomials and Rational Expressions

Interpret the structure of expressions.

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Understand the relationship between zeros and factors of polynomials.

Use polynomial identities to solve problems.

Rewrite rational expressions.

Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]

Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

Interpreting functions

Interpret functions that arise in applications in terms of the context.

Analyze functions using different representations.

Building Functions

4.5 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); and the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Find inverse functions.

Linear, Quadratic and Exponential Models

Trigonometric Functions

Expressing Geometric Properties with Equations

Interpreting Categorical and Quantitative Data

Making Inferences and Justifying Conclusions

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Using Probability to Make Decisions