Semester Exam Review of Standards 36 and 37

Front

What is the definition of the Least Common Denominator (LCD)?

Back

The Least Common Denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.

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Back

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines that a graph approaches but never touches or crosses, typically occurring where a function is undefined.

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How do you determine vertical asymptotes from a rational function?

Back

Set the denominator equal to zero and solve for the variable.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How do you check for extraneous solutions?

Back

Substitute the solution back into the original equation to see if it holds true.

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What is the process for solving a complex fraction?

Back

Find the LCD of all fractions involved, multiply through by the LCD to eliminate the fractions, and then solve the resulting equation.

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What is the significance of the graph of a function in relation to its equation?

Back

The graph visually represents the behavior of the function, including intercepts, asymptotes, and overall shape.

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

Back

A horizontal asymptote indicates the value that a function approaches as the input approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: if the degree of the numerator is less, the asymptote is y=0; if equal, y=leading coefficient ratio; if greater, no horizontal asymptote.