Properties of Functions Review

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

Define domain in the context of functions.

Back

The set of all possible input values (x-values) for a function.

Front

Define range in the context of functions.

Back

The set of all possible output values (y-values) for a function.

Front

What does it mean for a function to be defined for all real numbers?

Back

It means that the function has an output for every possible real number input.

Front

What is a mapping diagram?

Back

A visual representation of a function that shows how each input is paired with an output.

Front

What is the significance of the origin (0,0) in functions?

Back

The origin is the point where the x-axis and y-axis intersect. A function can pass through the origin, indicating that f(0) = 0.

Front

What does it mean if a function is not defined at a certain point?

Back

It means that there is no output for that input value, often due to division by zero or taking the square root of a negative number.

Front

What is a piecewise function?

Back

A function that is defined by different expressions for different intervals of the input.

Front

How can you determine if a graph represents a function?

Back

By using the vertical line test; if a vertical line crosses the graph more than once, it is not a function.