Math 3 Review: Rationals/General Functions

Front

What is the formula to find the time taken when two people work together?

Back

If person A can complete a task in 'a' hours and person B can complete it in 'b' hours, the time taken to complete the task together is given by: 1/(1/a + 1/b) hours.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term. If the leading coefficient is positive and the degree is even, both ends go up. If the leading coefficient is negative and the degree is even, both ends go down. If the degree is odd, one end goes up and the other goes down.

Front

What is an asymptote in a function?

Back

An asymptote is a line that a graph approaches but never touches. Vertical asymptotes occur where the function is undefined, and horizontal asymptotes describe the behavior of the function as x approaches infinity.

Front

How do you find the intervals where a function is increasing or decreasing?

Back

To find intervals of increase or decrease, take the derivative of the function. Set the derivative to zero to find critical points, then test intervals around these points to determine where the function is increasing (positive derivative) or decreasing (negative derivative).

Front

What is the relationship between the rates of work for two people?

Back

The combined rate of work for two people is the sum of their individual rates. If Alex can paint a room in 9 hours, his rate is 1/9 rooms per hour. If Dawn's rate is unknown, together they can paint at a combined rate.

Front

How do you calculate the combined work rate of two individuals?

Back

If person A can complete a task in 'a' hours and person B can complete it in 'b' hours, their combined work rate is 1/a + 1/b tasks per hour.

Front

What does it mean for a function to have a horizontal asymptote?

Back

A horizontal asymptote indicates the value that a function approaches as x approaches infinity or negative infinity. It shows the long-term behavior of the function.

Front

What is the significance of critical points in a function?

Back

Critical points are where the derivative is zero or undefined. They are important for determining local maxima and minima, as well as intervals of increase and decrease.

Front

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

Back

Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero, provided that the numerator is not also zero at those points.

Front

What is the difference between a function's domain and range?

Back

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values) that the function can produce.