Understanding Constant Functions

The video tutorial explains the concept of constant functions, where the output remains the same regardless of the input. It uses the example of f(x) = 5 to illustrate that the output is always 5, no matter the input value. The graph of a constant function is a horizontal line parallel to the x-axis. The tutorial generalizes this concept with f(x) = K, where K is any real number, and concludes with a summary of the key points.

What is a constant function?

• A function that changes with input

• A function that remains the same for any input

• A function that is always zero

• A function that depends on the x-axis

In a constant function, what happens to the output when the input changes?

• The output changes

• The output becomes zero

• The output remains constant

• The output depends on the input

If f(x) = 5, what is the output when x = -1.7?

• -1.7

• 5

• 1.7

• 0

How is the graph of a constant function oriented?

• Perpendicular to the x-axis

• Parallel to the x-axis

• Diagonal to the x-axis

• Parallel to the y-axis

What is the vertical distance of the line from the x-axis in the graph of f(x) = 5?

• 5 units

• 1 unit

• 0 units

• 10 units

How can a constant function be generalized?

• f(x) = 0

• f(x) = K, where K is a real number

• f(x) = x

• f(x) = x + K

What does K represent in the general form of a constant function?

• A variable

• A constant real number

• The y-coordinate

• The x-coordinate

What is the shape of the graph of a constant function?

• A diagonal line

• A vertical line

• A curve

• A horizontal line

What is the equation of a constant function graph?

• y = mx + c

• y = x

• y = 0

• y = K

What is the significance of the constant K in f(x) = K?

• It determines the slope

• It determines the x-intercept

• It determines the y-intercept

• It determines the constant output value