Nonlinear Functions

Exponential functions such as $f(x)=a(b)^x$ are interpreted using the initial value $a$ and the growth or decay factor $b$. Values greater than 1 indicate growth, while values between 0 and 1 indicate decay.

Nonlinear function questions may involve transformed functions, vertices, zeros, symmetry, evaluating composite-looking expressions, or comparing function features from different forms.

Nonlinear functions include quadratic, exponential, polynomial, radical, and rational functions. SAT-style questions often ask for function values, intercepts, maximum or minimum values, vertex information, transformations, or the meaning of parameters in context.

Nonlinear functions include quadratic, exponential, polynomial, radical, and rational functions. SAT-style questions often ask for function values, intercepts, maximum or minimum values, vertex information, transformations, domain restrictions, or the meaning of parameters in context.

Nonlinear functions include quadratic, exponential, polynomial, radical, and rational functions. SAT-style questions often ask for function values, intercepts, maximum or minimum values, vertex information, transformations, domain restrictions, or the meaning of parameters in context.

Nonlinear functions include quadratic, exponential, polynomial, radical, and rational functions. SAT-style questions often ask for function values, intercepts, maximum or minimum values, vertex information, transformations, domain restrictions, or the meaning of parameters in context.

Nonlinear functions include quadratic, exponential, polynomial, radical, and rational functions. SAT-style questions often ask for function values, intercepts, maximum or minimum values, vertex information, transformations, domain restrictions, or the meaning of parameters in context.

Parameter questions for nonlinear functions may use vertex form, domain restrictions, exponential factors, or input-output conditions.

Function questions involving radicals and rational expressions often ask for a value, an excluded input, or an endpoint of the domain. The key restrictions are that square-root radicands must be nonnegative and denominators cannot equal zero.

Polynomial function questions often use factored form to identify zeros and standard form to identify intercepts or evaluate function values. Parameter questions may ask for a coefficient or constant from a known zero or value.

Quadratic functions can be interpreted through vertex, standard, and factored forms. Vertex form gives the vertex and maximum or minimum value, while factored form gives the zeros and the axis of symmetry.

Radical and rational functions often ask for domain restrictions, excluded inputs, and endpoint values. Square-root radicands must be nonnegative, and denominators cannot equal zero.