5.3 Linear vs Non-Linear Functions

Front

What is the definition of a linear function?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the definition of a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Its graph can be a curve, a circle, or any other shape that is not linear.

Tags

CCSS.8.F.A.3

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

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 crosses the graph more than once, then the graph does not represent a function.

Front

What is the significance of the x-value in a function?

Back

In a function, each x-value must correspond to exactly one y-value. If an x-value corresponds to multiple y-values, the relation is not a function.

Tags

CCSS.8.F.A.1

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if there exists at least one x-value that is associated with more than one y-value.

Tags

CCSS.8.F.A.1

Front

What are some common forms of nonlinear functions?

Back

Common forms of nonlinear functions include quadratic functions (e.g., f(x) = ax^2 + bx + c), exponential functions (e.g., f(x) = a * b^x), and trigonometric functions (e.g., f(x) = sin(x)).

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, represented by 'm' in the equation f(x) = mx + b. It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by 'b' in the equation f(x) = mx + b.

Front

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

Back

A function is linear if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2