HP Review for Midterm

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity. It indicates the behavior of the function at extreme values.

Front

What does it mean if a zero has an even multiplicity?

Back

If a zero has an even multiplicity, the graph of the function touches the x-axis at that zero but does not cross it. This indicates a turning point at that x-value.

Front

How do you find the domain of a rational function?

Back

To find the domain of a rational function, identify values of x that make the denominator zero, as these values are excluded from the domain.

Front

Back

Front

What are inverse functions?

Back

Front

How do you determine if two functions are inverses?

Back

Front

What is a difference quotient?

Back

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Back

Front

What does it mean for a function to have no horizontal asymptote?

Back

A function has no horizontal asymptote if it does not approach a specific value as x approaches positive or negative infinity. This often occurs in functions that grow without bound.

Front

What is the significance of a turning point on the x-axis?

Back

A turning point on the x-axis indicates that the function has a zero at that point, and the multiplicity of that zero is even, meaning the graph touches the x-axis but does not cross it.