Increasing and Decreasing Intervals

• Identify intervals of increasing/decreasing for function defined by ( f(x) = x^3 ).

Average Rate of Change

• Evaluate ( f(3) ) for the function ( f(x) = 4x^2 + 2 ).

• Find average rate of change over interval [2, 4] for ( f(x) = x + 1 ).

• For specific functions, compute average rates from given x values.

Polynomial Functions

• Find extremas of ( f(x) = x^4 + x ) and round to nearest thousandth.

• Write a polynomial of degree 4 with zeros at 1 and 4 (Multiplicity 2).

Function Properties

• Determine if functions are even, odd, or neither (e.g., for ( f(x) = 3x^2 )).

• Use sign analysis to solve inequalities.

Function Analysis

• Identify zeros and multiplicities for ( f(x) = k(x^2 + 3) ).

• Determine end behavior using limit notation.

Rational Function Characteristics

• Define domain, range, vertical and horizontal asymptotes for ( f(x) = \frac{x}{x^3 - 1} ).

• Find zeros and coordinates of holes.

• Write end behavior in terms of limits.

Binomial Expansion

• Apply binomial theorem to expand ( (x + 1)^n ).

Linear Models and Predictions

• Create linear model from data and use it for predictions (e.g., car valuation after years).

Volume and Domain Calculations

• Express volume of box as function ( V(x) ) given side cutouts.

• Determine the function's domain and maximum volume through graphing.

Population Models

• Model population growth with logistic functions (e.g., elk population).

Sequences

• General rules for arithmetic and geometric sequences.

• Identify terms in sequences and functions modeling their behavior.

Exponential Growth and Decay

• Analyze and differentiate exponential growth from decay functions.

Function Analysis and Inverses

• Examine transformation effects, domain/range, and derive inverse functions.

• Investigate logarithmic forms of exponents and solve equations logarithmically.

Residuals and Regression

• Solve for residuals in regression equations and interpret slope in context.