Unit 4: Rational Functions Flashcard

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

How do you find the combined work rate of two people working together?

Back

To find the combined work rate, add their individual rates. If person A can complete a task in time A and person B in time B, their combined rate is 1/A + 1/B.

Front

What is the formula for distance when speed and time are known?

Back

Distance = Speed × Time.

Front

How do you set up an equation for a boat's speed in still water given current speed?

Back

Let x be the speed of the boat in still water. The effective speed downstream is (x + current speed) and upstream is (x - current speed). Use these to set up the equation.

Front

What is the process for adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the significance of the average speed in a travel problem?

Back

Average speed is crucial for determining travel time and understanding the relationship between distance, speed, and time.

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator and cancel out any common factors.

Front

What does it mean for a speed to be 'faster' in a travel problem?

Back

A speed being 'faster' means it is greater than another speed, affecting the time taken to cover the same distance.

Front

What is the relationship between time, speed, and distance?

Back

The relationship is defined by the formula: Distance = Speed × Time, which can be rearranged to find any of the three variables.

Front

How do you determine the time taken for two people to complete a task together?

Back

Use the combined work rate formula: Time = 1 / (1/A + 1/B), where A and B are the times taken by each person individually.