Precalculus Final Exam - Fall 2024

Front

What is a removable discontinuity in a function?

Back

A removable discontinuity occurs at a point where a function is not defined due to a factor in the numerator and denominator that can be canceled out, resulting in a hole in the graph.

Front

How do you find holes in a rational function?

Back

To find holes, factor both the numerator and denominator, identify common factors, and set them equal to zero. The x-values where these factors equal zero are the locations of the holes.

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator equal to zero and solve for x, ensuring that the factor is not removable.

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

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

Front

What is the significance of the leading coefficient in determining horizontal asymptotes?

Back

The leading coefficient of the highest degree term in the numerator and denominator determines the value of the horizontal asymptote when the degrees are equal.

Front

What does it mean if a function has no holes?

Back

If a function has no holes, it means there are no common factors in the numerator and denominator that can be canceled out.

Front

What is the difference between removable and non-removable discontinuities?

Back

Removable discontinuities can be 'fixed' by redefining the function at that point, while non-removable discontinuities cannot be removed and indicate vertical asymptotes.

Front

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

Back

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