Functions, Functions, 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

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it assigns a unique output for every unique input, meaning no two different inputs produce 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 does h(t) represent in the context of functions?

Back

h(t) represents the output of the function h for a given input t, often used to model real-world situations.

Front

If f(x) = 3x + 2, what is f(2)?

Back

f(2) = 3(2) + 2 = 8.

Front

What is an independent variable in a function?

Back

An independent variable is the variable that represents the input of a function, often denoted as x.

Front

What is a dependent variable in a function?

Back

A dependent variable is the variable that represents the output of a function, often denoted as y, and depends on the independent variable.

Front

What is a linear function?

Back

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