Functions

What is the definition of a function?

A relation where every input (x) has exactly one unique output (y).

What does "domain" mean?

The complete set of all possible input values (x-coordinates).

What does "range" mean?

The complete set of all possible output values (y-coordinates).

In the function notation g(x) = 5x, what does g represent?

The name of the function.

What visual test determines if a graph is a function?

The Vertical Line Test.

If a vertical line crosses a graph twice, is it a function?

No, because one input has two different outputs.

Is the relation {(1, 2), (2, 3), (1, 4)} a function?

No, because the input 1 repeats with two different outputs (2 and 4)

Is the relation {(3, 5), (4, 5), (5, 5)} a function?

Yes, different inputs can share the same output.

If an x-value repeats in a data table with a different y-value, is it a function?

No.

On a graph, where do you look to find the y-intercept of a function?

Where the graph crosses the vertical y-axis (where x = 0).

What is the domain of a horizontal line segment spanning from x = -2 to x = 5 (including endpoints)?

-2 < x < 5

What is the range of a vertical line segment spanning from y = 1 to y = 6 (including endpoints)?

1 < y < 6

If a graph goes up from left to right, is it increasing or decreasing?

Increasing

If a function graph is a straight line, what type of function is it?

A Linear Function.

What parent function creates a U-shaped graph (parabola)?

The quadratic function (f(x) = x²)