AP Precalculus Full Review Flashcards

Flashcards of key vocabulary terms from an AP Precalculus review.

Function

A mathematical relation where there is a set of input x's and output y values such that each input value is mapped to one exact output value.

Domain

The input values of a function; the independent variable.

Range

The output values of a function; the dependent variable.

Increasing Function

A function where as the input values increase, the output values always increase.

Decreasing Function

A function where as the input values increase, the output values always decrease.

Rate of Change

A graph's slope.

Concave Up

When the rate of change is increasing or when the graph looks like a U.

Concave Down

When the rate of change is decreasing and it looks like an upside-down U.

Zeros of the Function

Whenever a graph intersects the x-axis, the output value or y value is zero, meaning the corresponding x's or input values.

Y-intercept

The point where the graph crosses the y-axis.

Positive Rate of Change

A positive rate of change means that as one quantity increases or decreases, the other quantity does the same.

Negative Rate of Change

A negative rate of change means that as one quantity increases, the other decreases.

Linear Function Rate of Change

In a linear function, the rate of change will always be the same no matter what interval you assign to it.

Quadratic Function Rate of Change

In quadratic functions, the average rate of change is changing at a linear rate.

Absolute Maximum

Of all local maximums, the greatest.

Absolute Minimum

The least of all local minimums.

Points of Inflection

Points of inflection of a polynomial function occur at input values where the rate of change of the function changes from increasing to decreasing or from decreasing to increasing.

Degree of a Polynomial Function

The highest value of the exponent in a polynomial function.

Even Function

A function where f(x) = f(-x) or if reflected across the y-axis, the graph looks the exact same.

Odd Function

A function where f(x) = -f(-x) or if rotated across the origin 180°, it remains looking the exact same.

End Behavior

Describes how the graph ends on both the left and right side.

Asymptote

An invisible line that values of the graph will continue to get close to but will never touch.

Vertical Asymptote

An invisible line that the graph will keep trying to approach but will never reach, all the way to positive or negative infinity.

Hole

A spot that occurs at a graph when in the equation, once you solve the numerator and denominator, you get a common factor between the two.

Additive Transformations: g(x) = f(x) + k, g(x) = f(x - k)

Adding either up/down or left/right to the function.

Multiplicative Transformations: g(x) = a f(x), g(x) = f(bx)

Vertical and horizontal dilation of the function.

Regression

A pattern that is used the determine the model that matches a scenario with the best R value.

Sequence

A list of numbers.

Arithmetic Sequence

A type of sequence that is really just a linear function whose numbers have a common rate of change with a common difference.

Geometric Sequence

A type of sequence that increases more and more as the sequence continues because of a common proportional change.

Rules of Exponential Functions

For an exponential function, a cannot equal zero, b must always be positive, and b can never be one.

Exponential Growth

An exponential function that happens when a is greater than zero and b is greater than one.

Exponential Decay

An exponential function that happens when a is greater than zero and b is less than one but greater than zero.

Product Property of Exponents

If you multiply two values with an exponent that have the same base, then you are really just adding their exponents (b^m * b^n = b^(m + n)).

Power Property of Exponents

If you have double exponents, you are simply multiplying the exponents together. (b^m to the power of n is equal to b^(mn)).

Negative Exponent Property

If you ever have a negative exponent, it is simply equal to 1 over the original term, removing the negative sign on the exponent. (b^n = 1 / b^n).

Exponent Root Property

If you ever have a power that is 1 over something, it's really asking you to do what the denominator's root of the function is. (b^(1/k) is equal to the k-th root of b).

Residual

The difference between the actual data point and the value predicted by your model.

Inverse Function

An inverse is typically notated like instead of f(x) being f^(-1)(x).

Rule of Inverse Functions

For a function to have an inverse function, it must be one-to-one, meaning each output value is produced by exactly one input value.

Log Form

If you had the expression 2^x = 8, you can infer that x = 3. But to rearrange this into log form, we say log base 2 of 8 = 3.

Semi-log Plot

a plot that either has the x or y-axis logarithmically scaled while the other axis remains linearly scaled.

Periodic Graph

For a graph to be periodic, it has to have a continuous cycle of the same pattern happen over and over over equal length intervals.

Period

How long it takes a graph to complete one cycle.

Sine

Sine deals with a vertical displacement, which is y/r.

Cosine

Cosine deals with the horizontal displacement, which is x/r.

Tangent

Tangent deals with the slope, meaning rise over run or y/x.

Sinosoidal Function

A periodic function that continuously oscillates between a set minimum and maximum point.

Amplitude of a Sinosoidal Function

The horizontal distance from the middle line to the maximum point on the graph.

Phase Shift

moves the graph by -C units left or right.

Polar Funtions

In polar functions, the radius is how far the circles go out and the theta is determining what angle that coordinates is in.

Crossing The Pole

Flip the negative point across the origin.

Polar Function Increase/Decrease

If r is positive and increasing, the point moves away from the origin. If r is negative and decreasing, the point also moves away because it's flipping direction. If r is positive and decreasing, the point moves toward the origin. If r is negative and increasing, the point also moves toward the origin.