Identifying Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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 the definition of a function?

Back

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

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input (x) is associated with more than one output (y).

Front

What is the slope of a linear function?

Back

The slope (m) of a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

What is the y-intercept of a linear function?

Back

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

Front

How do you determine if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line. If the graph curves or bends, it is not linear.

Front

What is the difference between linear and non-linear functions?

Back

Linear functions create straight lines when graphed, while non-linear functions create curves or other shapes.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

Front

What is an example of a non-linear function?

Back

An example of a non-linear function is f(x) = x^2, which creates a parabolic curve when graphed.