Polynomial, rational, radical, and exponential functions
- transformations
- zeros
- inverse relationships
- asymptotes
Grade 11 / Algebra II · typical sequence
Grade 11 advanced algebra pathway
Extend function families, complex numbers, polynomial and rational structure, and quantitative modeling.
Complex numbers and algebraic structure
- complex arithmetic
- polynomial identities
- rational equations
Sequences, probability, and data models
- arithmetic and geometric sequences
- conditional probability
- regression
Practice inventory
18 deterministic activities are available now.
Transform a function graph
Connect changes inside and outside function notation to horizontal and vertical graph changes.
Predict polynomial end behavior
Use the parity of the degree and sign of the leading term to predict both ends of a polynomial graph.
Find polynomial zeros
Read every linear factor as a zero and retain all real solutions.
Use the Remainder Theorem
Recognize that dividing by x minus a leaves remainder p of a.
Add complex numbers
Treat real parts and imaginary parts as separate like-term groups.
Multiply complex numbers
Distribute complex factors and replace i squared with negative one before combining terms.
Find complex quadratic roots
Interpret a negative radicand with i and keep both square-root branches.
Recognize a polynomial identity
Match expanded and factored structures by distribution rather than surface resemblance.
Simplify a rational expression
Cancel common factors while retaining excluded domain values.
Solve a rational equation
Clear denominators, solve the resulting equation, and reject values outside the original domain.
Solve a radical equation
Square only after isolating the radical and verify the result in the original equation.
Find an inverse function
Exchange input and output, then solve for the new output.
Compose two functions
Use the inner output as the outer input without combining unrelated rules.
Solve an exponential equation
Rewrite compatible bases or apply the inverse relationship between exponents and logarithms.
Evaluate a geometric sequence
Use an initial term and common ratio in an explicit geometric sequence rule.
Find a conditional probability
Use only the conditioned group as the denominator and count its overlap with the target event.
Use the probability addition rule
Add two event probabilities and subtract their shared intersection once.
Interpret a model residual
Compute observed minus predicted and interpret the sign as above or below the model.