Rational Word Problems and graphs

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

Front

How do you find the common denominator in rational expressions?

Back

To find the common denominator, identify the least common multiple (LCM) of the denominators of the rational expressions involved.

Front

What is an asymptote in a graph?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

How do you solve a rational equation?

Back

To solve a rational equation, first find a common denominator, multiply both sides by it to eliminate the fractions, and then solve the resulting equation.

Front

What is the significance of the vertical asymptote?

Back

The vertical asymptote indicates the values of x where the function is undefined and the graph approaches infinity.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator of a rational expression equals zero.

Front

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

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What is the formula for work done together by two people?

Back

If person A can complete a job in 'a' hours and person B in 'b' hours, their combined work rate is given by 1/a + 1/b = 1/t, where t is the time taken together.

Front

What is the first step in solving a rational word problem?

Back

The first step is to define the variables and set up an equation based on the information provided in the problem.

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.