Linear vs. Nonlinear Functions Day 3

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in the form y = 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 rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

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, the graph does not represent a function.

Front

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

Back

If a graph is not a function, it means that for at least one input value (x), there are multiple output values (y). This violates the definition of a function, which states that each input must correspond to exactly one output.

Front

How can you tell if a table represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the slope of a linear function?

Back

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

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. It is the value of y when x = 0.

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3. Its graph is a straight line with a slope of 2 and a y-intercept of 3.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2. Its graph is a parabola, which is not a straight line.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.