Exploring Piecewise Functions

This video tutorial explains how to graph piecewise defined functions through various examples. It covers graphing linear, constant, quadratic, and square root functions, emphasizing the conditions under which each piece of the function is valid. The tutorial provides step-by-step instructions on plotting points, drawing lines, and ensuring endpoints are correctly represented as open or closed based on the function's conditions.

What is the y-intercept of the linear function f(x) = 4/5x + 1?

• (0, 1)

• (1, 0)

• (4, 0)

• (0, 4)

For the function f(x) = 4/5x + 1, what should be done with values of x that are 0 or more?

• Ignore them

• Highlight them

• Erase them

• Include them

What is the slope of the linear function in the second example?

• -3/2

• -2/3

• 3/2

• 2/3

In the second example, what is the y-value when x = 2 for the quadratic function?

• -4

• 5

• 3

• 0

What is the y-value when x = 0 for the quadratic function in the third example?

• 0

• -4

• 4

• 1

In the third example, what is the y-value when x = 3 for the quadratic function?

• 5

• -3

• 1

• 0

For the linear function in the fourth example, what is the y-value when x = 2?

• -3

• 2

• 0

• 3

In the fourth example, what is the y-value when x = 3 for the quadratic function?

• 2

• -3

• 0

• 3

In the fifth example, what is the y-value when x = -4 for the absolute value function?

• 3

• 0

• 1

• 2

For the square root function in the fifth example, what is the y-value when x = 8?

• 1

• 2

• 3

• 4