Constant Functions and Their Properties

The video tutorial introduces the concept of constant functions, explaining that these functions map every element of the domain to a single, constant value. It defines constant functions as those where the output remains the same regardless of the input. The tutorial provides examples to illustrate this concept and demonstrates how constant functions appear as horizontal lines on a graph. The properties of constant functions are discussed, emphasizing that the y-value remains constant across all x-values, extending to positive and negative infinity.

What is a constant function?

• A function that changes outputs randomly.

• A function where each input has a unique output.

• A function where all inputs map to the same output.

• A function with no outputs.

In a constant function, what is true about the domain elements?

• Domain elements have no images.

• All domain elements map to a single unique image.

• Domain elements map to multiple images.

• Each domain element maps to a different image.

How is a constant function typically expressed mathematically?

• f(x) = x^2

• f(x) = x + c

• f(x) = constant

• f(x) = x - c

What happens when different values are input into a constant function?

• The output changes with each input.

• The output remains the same for all inputs.

• The output depends on the input.

• The output is undefined.

What does the graph of a constant function look like?

• A vertical line.

• A straight horizontal line.

• A zigzag line.

• A curved line.

Why is the graph of a constant function a straight line?

• Because it has no x-intercept.

• Because the y-value changes with x.

• Because the y-value is constant for all x.

• Because the x-value is constant for all y.

What is an example of a constant function?

• f(x) = x + 3

• f(x) = 3

• f(x) = x^2

• f(x) = x - 3

What is the y-value for a constant function f(x) = 5?

• It depends on the domain.

• It varies with x.

• It is always 0.

• It is always 5.

How does a constant function behave as x approaches infinity?

• The y-value becomes undefined.

• The y-value remains constant.

• The y-value decreases.

• The y-value increases.

What is the domain of a constant function?

• Only integers.

• All real numbers.

• Only positive numbers.

• Only negative numbers.