Front

What is a hole in a graph?

Back

A hole in a graph occurs at a point where the function is not defined, typically due to a factor in the numerator and denominator that cancels out.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the degree of the polynomial function P(x)=3x^4-7x^2-2x^7-x+4?

Back

The degree is 7, as the highest power of x is 7.

Front

What is a rational inequality?

Back

A rational inequality is an inequality that involves a rational expression, which is a fraction where the numerator and denominator are polynomials.

Front

How do you solve the rational inequality \( \frac{x-3}{x-1}<0 \)?

Back

To solve, find the critical points where the expression equals zero or is undefined, then test intervals to determine where the inequality holds.

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

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

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, the asymptote is y=0; if equal, y=leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What does it mean for a function to be undefined at a certain point?

Back

A function is undefined at a point if substituting that point into the function results in division by zero or an indeterminate form.

Front

What is the significance of the x-intercepts of a polynomial function?

Back

The x-intercepts are the points where the graph of the polynomial crosses the x-axis, indicating the values of x for which the polynomial equals zero.