Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x) for a function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y) for a function.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, typically in the form y = mx + b.

Front

What is the slope in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how steep the line is.

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the output when x = 0.

Front

How do you find f(5) if f(x) = 3x - 9?

Back

Substitute 5 for x: f(5) = 3(5) - 9 = 15 - 9 = 6.

Front

What is the algebraic equation for a linear function represented by the table?

Back

The equation can be derived from the pattern in the table; for example, y = x - 3.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions create straight lines, while nonlinear functions create curves or other shapes.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.