Graphing Rational expressions

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a value of x where both the numerator and denominator are zero, indicating that the function is undefined at that point.

Front

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

Back

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

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you identify vertical asymptotes in a rational function?

Back

Vertical asymptotes can be found by setting the denominator equal to zero and solving for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

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

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator.

Front

What is the degree of a polynomial?

Back

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

Front

What happens to the graph of a rational function at a hole?

Back

At a hole, the graph will not be defined, and there will be a gap in the graph at that x-value.

Front

What is the significance of x-intercepts in graphing?

Back

X-intercepts indicate where the graph crosses the x-axis, showing the values of x for which the function equals zero.

Front

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, evaluate the function at x = 0.