AP Precalculus Unit 1 Refresh

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes for rational functions?

Back

For rational functions, horizontal asymptotes can be found by comparing the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If they are equal, the asymptote is y=\frac{a}{b}, where a and b are the leading coefficients.

Front

What is an inflection point?

Back

An inflection point is a point on the graph of a function where the concavity changes, indicating a transition from concave up to concave down or vice versa.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first point.

Front

What does it mean for a function to be positive?

Back

A function is positive on an interval if its values are greater than zero for all points in that interval.

Front

How do you determine the intervals where a function is increasing or decreasing?

Back

To determine intervals of increase or decrease, find the derivative of the function. The function is increasing where the derivative is positive and decreasing where the derivative is negative.

Front

What is the significance of critical points?

Back

Critical points are values of x where the derivative is zero or undefined. They are important for finding local maxima, minima, and points of inflection.

Front

What is the relationship between the first derivative and the graph of a function?

Back

The first derivative of a function indicates the slope of the tangent line to the graph. A positive derivative indicates the function is increasing, while a negative derivative indicates it is decreasing.

Front

What is the relationship between the second derivative and concavity?

Back

The second derivative indicates the concavity of the function. If the second derivative is positive, the function is concave up; if negative, it is concave down.