Final Review - Pre-Cal - S1

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What is a Horizontal Asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity. For example, for the function f(x) = 1/(x-1), the horizontal asymptote is y = 0.

Front

What does it mean if a function exhibits exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value. For example, in the function f(t) = a * e^(-kt), the value decreases over time.

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How can you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant. For example, in the sequence 37, 31, 25, 19, the common difference is -6.

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Back

The graph of the function is an exponential curve that increases rapidly as x increases, starting from a value of 0.45 when x=0.

Front

What is a common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by. For example, in the sequence -19, -15, -11, -7, -3, the common difference is +4.

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How do you find the number of sequences with a specific common difference?

Back

To find the number of sequences with a specific common difference, check each sequence to see if the difference between consecutive terms is equal to that common difference.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

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What is the difference between exponential growth and decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when it decreases at a rate proportional to its current value.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, indicating the value of the function when x = 0.

Front

How do you identify the vertical asymptote of a rational function?

Back

The vertical asymptote of a rational function occurs where the denominator equals zero, provided that the numerator does not also equal zero at that point.