8 Lesson 23 - Identifying Linear and Nonlinear 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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be curved or have varying slopes.

Front

How can you identify a linear function from its equation?

Back

If the equation can be written in the form f(x) = mx + b, it is a linear function. If it includes variables multiplied together or raised to a power, it is nonlinear.

Front

What does the slope of a linear function represent?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

Evaluate the function f(x) = 2x + 2 for x = 4.

Back

f(4) = 2(4) + 2 = 10.

Front

Is the function f(x) = x^2 a linear or nonlinear function?

Back

Nonlinear, because it includes x raised to the power of 2.

Front

Determine if the graph of y = 4x + 6 is linear or nonlinear.

Back

Linear, because it can be represented as a straight line.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

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

Back

It means that there is at least one input that corresponds to more than one output.