Functions: Graphing and Translations Flashcard

Front

What is the y-intercept?

Back

The y-intercept is the point where the graph of a function intersects the y-axis. It is represented as a coordinate (0, b), where b is the value of the function when x = 0. Example: For the function y = 2x + 3, the y-intercept is (0, 3).

Front

What is the x-intercept?

Back

The x-intercept is the point where the graph of a function intersects the x-axis. It is represented as a coordinate (a, 0), where a is the value of the function when y = 0. Example: For the function y = x - 10, the x-intercept is (10, 0).

Front

Solve for x: ax + c = R

Back

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Example: In the sequence 2, 6, 18, 54, the common ratio is 3.

Front

What is the explicit formula for the nth term of a geometric sequence?

Back

Front

Write the exponential equation that represents the given table: (0, 80), (1, 20), (2, 5), (3, 1.25)

Back

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input and f(x) is the output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. Example: For the function f(x) = \sqrt{x}, the domain is x ≥ 0.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. Example: For the function f(x) = x^2, the range is y ≥ 0.

Front

What does it mean to translate a graph?

Back

Translating a graph means shifting it horizontally, vertically, or both without changing its shape. Example: The graph of y = f(x) + k is a vertical translation of f(x) by k units.