AP Precalculus Flashcards

Flashcards for key vocabulary and concepts in AP Precalculus, covering polynomial, rational, exponential, logarithmic, and trigonometric functions.

Average Rate of Change (AROC)

Slope of the secant line between two points (a, f(a)) and (b, f(b)). Formula: (f(b) - f(a)) / (b - a)

Secant Line

A line formed between two points 'a' and 'b' using the Average Rate of Change formula.

Odd Function

Function where f(-x) = -f(x). It passes through the origin.

Even Function

Function where f(-x) = f(x). It reflects over the y-axis.

Let y = 0

x-intercept

Let x = 0

y-intercept

Complex Conjugate

If a + bi is a factor, then a - bi is also a factor.

End Behavior

Describes the behavior of a function as x approaches infinity or negative infinity.

Limit Notation: lim (x→c) f(x) = L

Mathematical notation to describe the limit of a function f(x) as x approaches c, equaling L.

a-value (Transformation)

Vertical reflection across x-axis for a < 0; Vertical dilation by factor of |a|.

b-value (Transformation)

Horizontal dilation by a factor of 1/|b|.

h-value (Transformation)

Horizontal translation in the direction of -h.

k-value (Transformation)

Vertical translation; Up +k, Down -k.

Vertical Asymptote

When a factor in the denominator does not cancel out.

Horizontal Asymptote Cases (n, m are degrees of numerator and denominator)

If n < m, then y = 0; if n = m, then y = a/b.

Hole (in a rational function)

Occurs when a common factor cancels out after simplifying the rational expression.

Arithmetic Sequences (Linear)

Sequences that have the same differences between terms (add).

Geometric Sequences (Exponential)

Sequences that have common ratios between consecutive terms.

Logarithmic Functions

Input values change proportionally for consistent output values

Inverse Functions

Input values and output values are switched.

Semi-Log Plots

The y-axis is a logarithmic scale, usually powers of 10.

tan(𝜃)

sin(𝜃) / cos(𝜃)

csc (𝑥)

1 / sin(𝑥)

sec (𝑥)

1 / cos(𝑥)

cot (𝑥)

cos(𝑥) / sin(𝑥)

Polar to Rectangular Coordinates

x = r cos 𝜃, y = r sin 𝜃

Rectangular to Polar Coordinates

r^2 = x^2 + y^2, tan 𝜃 = y/x

Rose Curves

Graphs that are rose shaped. In 𝑛 ≠ 0 is even, the rose has 2𝑛 petals; if 𝑛 ≠ ±1 is odd, the rose has 𝑛 petals, for 𝑎 ≠ 0.

D-value (Sinusoidal Transformation)

Vertical shift; midline of sinusoidal functions.

B-value (Sinusoidal Transformation)

Number of cycles in 2π

sin(A+B)

sin(A)cos(B) + cos(A)sin(B)

cos(A-B)

cos(A)cos(B) + sin(A)sin(B)