AP Precalc Justification Guide

f is best modeled by a linear function

Over consecutive equal-length input-value intervals of

size ___, there is a constant difference in output values

of ____.

f is best modeled by a quadratic function

Over consecutive equal-length input-value intervals of

size ___, there is a constant second difference in

output values of ____.

f is best modeled by an exponential function

Input values change additively in intervals of size

_____ as output values change proportionally by a

factor of ____.

f is best modeled by a logarithmic function

Input values change proportionally by a factor of ____

as output values change additively in intervals of size

___.

A function f is invertible

Each input value of f has a unique output value. There

are no repeated f x( ) values.

f is postive

The graph of f is above the x/t axis

f is negative

The graph of f is below the x/t axisf is increasing

f is increasing

on an open interval I, a + b on I, with a<b, f(a) < f(b)

f is decreasing

on an open interval I, a + b on I, with a<b, f(a) > f(b)

The rate of change of f is postive

F is concave up

The rate of change of f is negative

f is concave down

f is concave up

Average rates of change of f over equal-sized intervals

are increasing.

f is concave down

Average rates of change of f over equal-sized intervals

are decreasing.

The graph of f has a hole at x = a

The multiplicity of x=a in the numerator is greater

than or equal to the multiplicity of x = a in the

denominator.

The graph of f has a vertical asymptote at x = a

x=a is a zero of the denominator and NOT of the

numerator

OR

The multiplicity of x=a in the denominator is greater

than or equal to the multiplicity of x = a in the

numerator.

The graph of f has an x-intercept at x = a

x=a is a zero of the numerator and NOT of the

denominator

f has a relative maximum at x = a

f changes from increasing to decreasing at x=a

OR

The rate of change of f changes from positive to

negative at x=a

OR

On a closed interval [a,b], either f (a) or f (b) is greater

than all function values in the neighborhood of a or b,

respectively.

f has a relative minimum at x = a

f changes from decreasing to increasing at x=a

OR

The rate of change of f changes from negative to

positive at x=a

OR

On a closed interval [a,b], either f (a) or f (b) is less

than all function values in the neighborhood of a or b,

respectively.

f has an absolute maximum at x = a

The greatest of all local/relative maxima

f has an absolute minimum at x = a

The least of all local/relative minima

A model is considered appropriate for a data set

The residual plot for the model appears without

pattern