AP Precalculus Video Notes: Functions, Rates of Change, Polynomials, and End Behavior (Flashcards)

15 practice Q&A flashcards covering function basics, rate of change, polynomial concepts, and end behavior as described in the notes.

What is a function?

A mathematical relation that maps inputs to outputs with each input value mapped to exactly one output value.

What is the independent variable in a function?

The input value, usually denoted x (or time t in some examples).

What is the dependent variable in a function?

The output value, usually denoted y.

In the pool example w(x), what does x represent?

The length of the pool (the input variable for the function giving water in gallons).

What are the four ways to represent a function mentioned in the notes?

Verbally, analytically, numerically, or graphically.

What does increasing mean in words?

As the input values increase, the output values increase.

What does decreasing mean in words?

As the input values increase, the output values decrease.

What is the formula for the average rate of change on [a, b]?

(f(b) − f(a)) / (b − a), the slope of the secant line between (a, f(a)) and (b, f(b)).

How can you approximate the rate of change at a single point?

By using average rates of change over small intervals that contain the point.

What is true about the average rate of change for a linear function?

It is constant for any interval.

What is end behavior in a polynomial?

The behavior of P(x) as x approaches ±∞, determined by the leading term (the term with the highest degree).

End behavior for even degree with positive leading coefficient?

Both ends go to +∞ (left and right up).

End behavior for even degree with negative leading coefficient?

Both ends go to −∞ (left and right down).

End behavior for odd degree with positive leading coefficient?

Left end goes to −∞ and right end goes to +∞.

End behavior for odd degree with negative leading coefficient?

Left end goes to +∞ and right end goes to −∞.