T4: Interpreting Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one 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.

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.

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What does it mean for inputs to repeat in a function?

Back

If inputs repeat in a function, it means that the same input value is used more than once. For a relation to be a function, these repeated inputs must have the same output.

Front

What is the vertical line test?

Back

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

Front

What is the output of the function t(x) = x/8 + 2x when x = 16?

Back

t(16) = 34.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, because division by zero is undefined.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.