Unit 2 - AP Precalc

Flashcards covering key concepts from Unit 2 of AP Precalculus, including arithmetic and geometric sequences, exponential and logarithmic functions, compositions and inverses of functions, and data modeling.

Arithmetic Sequence

A sequence where the difference between consecutive terms is constant.

Geometric Sequence

A sequence where the ratio between consecutive terms is constant.

Exponential Functions

Functions where the independent variable appears in the exponent.

Compositions of functions

The operation of applying one function to the result of another.

Inverse Functions

A function that reverses the effect of another function.

Invertible

A function that has an inverse.

Logarithmic functions

Functions that are the inverse of exponential functions.

Residual Plot

A plot of the residuals against the predicted values.

Semi-log Plot

A plot where one axis is logarithmically scaled.

Linear Functions

Arithmetic Sequences relate to what type of functions?

Exponential Functions

Geometric Sequences relate to what type of functions?

The graph reflects over the x-axis.

What is the result of a vertical dilation by a factor of 'a' when a < 0?

(x + h)

What is the result of horizontal translation of 'h' units?

• k

What is the result of vertical translation of 'k' units?

f(d) = (2)^d

In context and data modeling, if a quantity doubles every day, what is the form of the exponential function?

The actual value minus the predicted value.

What does a residual represent in a regression model?

The residual plot has no pattern.

What signifies that a model is appropriate based on the residual plot?

Invertible (one-to-one)

Functions must be what for an inverse to exist?

b^a = c

If logb(c) = a, what is the exponential form?

b > 0, b ≠ 1

In y = logb(x), what are the restrictions?

Exponential Functions are always increasing or always decreasing, and their graphs are always concave up or always concave down

How exponential functions are described?

Logarithmic Functions are always increasing or always decreasing, and their graphs are always concave up or always concave down.

How logarithmic functions are described?

The outputs are proportional.

What characterizes exponential functions over equal intervals?

Over equal-length output-value intervals, the inputs are proportional

What is the property that demonstrate the outputs proportional in logarithmic functions?

Semi-log plots

The y-axis is logarithmically scaled and exponential data or functions appear linear in which plot?