AP Precalculus Unit 1 Refresh

Front

What is the interval where the function f(x) is positive and increasing?

Back

The function f(x) is positive and increasing on the interval (-5, -3) U (2, ∞).

Front

What do we call the point where concavity changes in a function?

Back

This point is called an Inflection Point.

Front

Given the polynomial function p(x) = -x(x-4)(x+2), what are the intervals where p(x) ≥ 0?

Back

The intervals where p(x) ≥ 0 are (-∞, -2] U [0, 4].

Front

What is the domain of a function that is undefined at x = -3?

Back

The domain is all real numbers x ≠ -3.

Front

What is the range of a function that is undefined at y = 1?

Back

The range is all real numbers y ≠ 1.

Front

How many extrema (maxima and minima) can be found in a given function graph if there are 3 turning points?

Back

There are 3 extrema in the graph.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form p(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is an inflection point in the context of calculus?

Back

An inflection point is a point on the curve of a function where the curvature changes sign.

Front

How do you determine the intervals of increase and decrease for a function?

Back

To determine the intervals of increase and decrease, find the first derivative of the function and analyze its sign.

Front

What is the significance of the first derivative test?

Back

The first derivative test helps to determine local maxima and minima of a function by analyzing the sign changes of the derivative.