AP PreCalculus Unit 1 Review

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. It indicates the behavior of the function at extreme values of x.

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator in a rational function. It represents a linear function that the graph approaches as x approaches positive or negative infinity.

Front

How do you determine the degree of a polynomial?

Back

Front

What does it mean for a polynomial to have end behavior of @@ ext{lim}_{x ightarrow- ext{infinity}}g(x)=- ext{infinity}@@?

Back

This means that as x approaches positive infinity, the value of the polynomial g(x) decreases without bound, indicating that the leading coefficient is negative and the degree is odd.

Front

Back

Finding intervals where one function is less than or equal to another helps identify where the graph of one function lies below or touches the graph of another, which is important for understanding their relationships.

Front

What is a residual in the context of a quadratic model?

Back

A residual is the difference between the observed value and the predicted value from a model. It indicates how well the model fits the data.

Front

How do you find the slant asymptote of a rational function?

Back

To find the slant asymptote, perform polynomial long division on the rational function. The quotient (ignoring the remainder) will give the equation of the slant asymptote.

Front

What is the end behavior of a polynomial with a positive leading coefficient and even degree?

Back

The end behavior will approach positive infinity as x approaches both positive and negative infinity.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers, while a rational function is a ratio of two polynomials.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).