HON. ALG.2: FLASHCARD Unit 2 Lessons 16-22

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where the function is undefined, typically where the denominator of a rational function equals zero.

Front

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

Back

To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for x.

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 determine the horizontal asymptote of a rational function?

Back

For rational functions, if the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is less than that of the denominator, the horizontal asymptote is y=0.

Front

What is the end behavior of a function?

Back

The end behavior of a function describes how the function behaves as x approaches positive or negative infinity.

Front

What does it mean for a function to approach a certain value as x increases?

Back

It means that as x gets larger, the output of the function gets closer and closer to that value, indicating a horizontal asymptote.

Front

What is the average cost function in a business context?

Back

The average cost function represents the total cost divided by the number of items produced, showing how cost per item changes with production volume.

Front

How do you write a function for average cost given fixed and variable costs?

Back

The average cost function can be written as C(x) = (fixed cost + variable cost per item * x) / x.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function and influences the direction of the graph as x approaches infinity.

Front

What is the difference between a vertical and horizontal asymptote?

Back

A vertical asymptote indicates where a function is undefined and approaches infinity, while a horizontal asymptote indicates the value the function approaches as x goes to infinity.