Identifying Linear Functions

Front

What is a linear function?

Back

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

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method used 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 does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements. This means each output is paired with exactly one input.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x). It indicates how much y changes for a given change in x.

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis. It is the value of y when x is 0.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, it is linear.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with an output. It helps to illustrate whether a relation is a function.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (usually x), while the dependent variable is the output (usually y) that depends on the input.