Graphs of rational functions

Front

What is a rational function?

Back

Tags

CCSS.HSF-IF.C.7D

Front

What are the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator Q(x) equal to zero, provided that these values do not also make the numerator P(x) equal to zero.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The horizontal asymptote can be found by comparing the degrees of the numerator and denominator: If the degree of P is less than the degree of Q, the asymptote is y=0; if they are equal, y=\frac{a}{b} where a and b are the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

Front

What is an x-intercept of a function?

Back

An x-intercept is a point where the graph of the function crosses the x-axis, which occurs when f(x) = 0.

Front

How do you determine the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator P(x) equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator, and it can be found using polynomial long division.

Tags

CCSS.HSF-IF.C.7D

Front

What does the term 'asymptote' mean in the context of graphs?

Back

An asymptote is a line that the graph approaches but never touches or crosses, indicating the behavior of the function as x approaches certain values.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the denominator in a rational function?

Back

The denominator determines the vertical asymptotes and the domain of the function, as it cannot be zero.

Tags

CCSS.HSF-IF.C.7D

Front

How can you identify the correct graph of a rational function?

Back

To identify the correct graph, analyze the function's asymptotes, intercepts, and end behavior, and compare these features with the options provided.

Tags

CCSS.HSF-IF.C.7D

Front

What is the domain of a rational function?

Back

The domain of a rational function consists of all real numbers except those that make the denominator zero.