Distinguishing Linear from Nonlinear Functions

Jimmy Chang explains how to distinguish between linear and nonlinear functions. Linear functions are characterized by a graph that forms a line and have a degree of 1, such as x to the first power. Nonlinear functions, on the other hand, do not form a line and can include curves, split graphs, and polynomials of higher degrees. Nonlinear functions can also include square roots, fractional exponents, and negative exponents. The video provides tips on identifying these functions based on their properties.

What is the main difference between linear and nonlinear functions?

• Linear functions are always horizontal.

• Nonlinear functions are always vertical.

• Nonlinear functions form a straight line, while linear functions do not.

• Linear functions form a straight line, while nonlinear functions do not.

Which of the following is NOT a characteristic of a linear function?

• It has a degree of 1.

• It can be represented by a straight line.

• It can be upward or downward sloping.

• It can be a vertical line.

What type of graph represents a nonlinear function?

• A horizontal line

• A curve

• A vertical line

• A straight line

Which of the following is an example of a nonlinear function?

• y = 3x - 1

• y = 5x

• y = x^2

• y = 2x + 3

What is the degree of a linear function?

• 1

• 0

• 2

• 3

Which of the following is NOT a polynomial?

• y = x^3

• y = x^2

• y = x^4

• y = sqrt(x)

What is an example of a nonlinear function with a negative exponent?

• y = x^-1

• y = x^2

• y = x + 1

• y = 2x

Which of the following is a characteristic of nonlinear functions?

• They are always horizontal.

• They can have exponents other than 1.

• They can be represented by a straight line.

• They have a degree of 1.

What is a key tip for distinguishing between linear and nonlinear functions?

• Linear functions can have any degree.

• Nonlinear functions are always horizontal.

• Linear functions have fixed properties.

• Nonlinear functions are always straight lines.