Flashcard Revew: Sequences - Piecewise - Abs. Value

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common difference in the sequence 26, 17, 8?

Back

The common difference is -9, calculated as 17 - 26 or 8 - 17.

Front

Find the 59th term of the arithmetic sequence 26, 17, 8.

Back

The 59th term is -496.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the main function's domain.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which interval the input value falls into and use the corresponding sub-function.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction.

Front

What is the equation of the absolute value function?

Back

The general form is f(x) = |x|.

Front

What does the graph of f(x) = |x| look like?

Back

The graph is a V-shape that opens upwards, with the vertex at the origin (0,0).

Front

How do you find f(-3) for the function f(x) = |x|?

Back

f(-3) = |-3| = 3.