AP Precalculus Ultimate Justification Guide Flashcards

Flashcards based on the AP Precalculus Ultimate Justification Guide for test preparation.

How do you justify that 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 _.

How do you justify that 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 _.

How do you justify that 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 ).

How do you justify that 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 ).

How do you justify that a function f is invertible?

Each output value of f is mapped from a unique input value. There are no repeated f(x) values.

How do you justify that the estimated output value found by using a known output and the average rate of change is an overestimate?

Secant line is above the curve at the input value of the estimate (Sketch a picture)

How do you justify that the estimated output value found by using a known output and the average rate of change is an underestimate?

Secant line is below the curve at the input value of the estimate (Sketch a picture)

How do you justify that f is positive?

The graph of f is above the x/t-axis

How do you justify that f is negative?

The graph of f is below the x/t-axis

How do you justify that f is increasing?

The graph of ƒ has a positive slope

How do you justify that f is decreasing?

The graph of f has a negative slope

How do you justify that the rate of change of f is increasing?

Average rates of change of f over equal-sized intervals are increasing

How do you justify that the rate of change of f is decreasing?

Average rates of change of f over equal-sized intervals are decreasing

How do you justify that f is concave up?

Average rates of change of f over equal-sized intervals are increasing.

How do you justify that f is concave down?

Average rates of change of f over equal-sized intervals are decreasing.

How do you justify that The graph off 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

How do you justify that 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 the multiplicity of x = a in the numerator

How do you justify that The graph of f has an x-intercept at x = a ?

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

How do you justify that f has a relative maximum at x = a?

f changes from increasing to decreasing at x = a OR The rate of change off changes from positive to negative at x = a

How do you justify that 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

How do you justify that A model is considered appropriate for a data set?

The residual plot for the model appears without pattern

How do you justify that The value predicted by the model at a certain input gives an overestimate for the true value at that input?

The residual for that input is negative

How do you justify that The value predicted by the model at a certain input gives an underestimate for the true value at that input?

The residual for that input is positive

How do you justify that The distance between a point on the graph of rf(0) and the origin is increasing?

Values of r are positive and increasing or values of r are negative and decreasing. (Ir❘ is increasing)

How do you justify that The distance between a point on the graph of r = f(0) and the origin is decreasing?

Values of r are positive and decreasing or values of r are negative and increasing. (Ir is decreasing)