Precalculus Review Flashcards

Flashcards based on precalculus lecture notes, covering functions, rates of change, exponents, logarithms and more.

What do the x's represent in a function?

Inputs (domain & independent)

What do the y's represent in a function?

Outputs (range & dependent)

What is the rate of change formula?

m = (y2 - y1) / (x2 - x1)

What is a positive rate of change?

As one quantity increases or decreases, the other quantity does the same.

What is a negative rate of change?

As one quantity increases, the other decreases.

What is the definition of a point of inflection?

Where the concavity of the graph changes from increasing to decreasing or vice versa.

What is multiplicity?

The amount of times a zero occurs in the equation.

What happens at a zero with even multiplicity?

The graph bounces at the x-axis.

What happens at a zero with odd multiplicity?

The line passes through the x-axis.

How to know if a function has an inverse?

If it passes the HLT, meaning each output is assigned to only one input value.

In exponential functions, what happens to output values?

Change at a proportional rate to input addition.

What are the properties of exponents?

Product, power, negative exponent properties.

What does f(g(x)) mean?

Plug in the g(x) equation wherever x appears in the f(x) equation.

What is the notation for a limit approaching infinity?

lim x -> ∞

What is vertical translation on a graph?

g(x) = f(x) + k

What is horizontal translation on a graph?

g(x) = f(x + k)

What is vertical dilation on a graph?

g(x) = a * f(x)

What is horizonal dilation on a graph?

g(x) = f(x*b)

What is an arithmetic sequence?

Linear sequence

What is a geometric sequence?

Exponential sequence

What is a rational function?

Polynomials divided by each other

What is the limit of a 'bottom heavy' rational function as x approaches infinity?

0

What is the horizontal asymptote if degree are same in a rational function?

leading coefficients divided by each other.

What does it mean if something gets 'crossed out' when simplifying rational functions?

There is a hole at that x-value

What does it mean if the degree of top is greater than the degree of the bottom?

The function has an obligue (or slant) asymptote.