Unit 4B Flashcard Review

Front

What is the relationship between Parker's and Libby's biking speeds if Parker rides 4 mph faster than Libby?

Back

If Parker's speed is represented as L + 4 (where L is Libby's speed), then the equation can be set up based on the distance and time they travel.

Front

How do you calculate the time it takes for two people to complete a task together?

Back

Use the formula: 1/(1/A + 1/B) = T, where A and B are the times taken by each person to complete the task alone, and T is the time taken together.

Front

What is a vertical asymptote in a rational function?

Back

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

Front

Back

Front

What is the significance of the degree of the numerator and denominator in determining horizontal asymptotes?

Back

The horizontal asymptote is determined by comparing the degrees: if the degree of the numerator is less than the denominator, the asymptote is y = 0; if they are equal, y = leading coefficient of numerator/leading coefficient of denominator.

Front

If Stephanie takes 7 hours and Shayna takes 12 hours to clean an attic, how do you find their combined work rate?

Back

Calculate their rates: Stephanie's rate = 1/7, Shayna's rate = 1/12. Combined rate = 1/7 + 1/12 = 1/T, where T is the time taken together.

Front

What is the formula for finding the time taken when two people work together?

Back

The formula is T = 1 / (1/A + 1/B), where A and B are the individual times taken by each person.

Front

What does it mean if a rational function has a hole?

Back

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

Front

Back

Since the degree of the numerator (0) is less than the degree of the denominator (2), the horizontal asymptote is y = 0.

Front

What is the process to solve for speeds when given distances and times?

Back

Use the formula: speed = distance/time. Set up equations based on the relationship between the speeds and distances.