Understanding Piecewise Functions

The video tutorial explains how to select a piecewise function based on its graph. It begins by describing the function's intervals and their characteristics, such as continuity and discontinuity. The first interval is identified as a square root function shifted to the left, while the second interval is a cubic function shifted to the right. The tutorial verifies these functions with specific x-values and concludes by selecting the correct piecewise function that matches the graph.

What is the range of x-values for which the piecewise function is undefined?

• x > -2 and x > 6

• x < -2 and x < 6

• x > -2 and x < 6

• x < -2 and x > 6

Which function represents the first part of the piecewise function?

• x^2 + 2

• sqrt(x) + 2

• sqrt(x + 2)

• x + 2

What is the value of the square root function at x = 2?

• 3

• 4

• 1

• 2

What type of function is the second part of the piecewise function?

• Exponential function

• Cubic function

• Linear function

• Quadratic function

What is the expression for the cubic function in the piecewise function?

• (x - 4)^3

• x^3 - 4

• (x + 4)^3

• x^3 + 4

At which x-value does the cubic function equal zero?

• x = 8

• x = 6

• x = 4

• x = 2

What is the value of the cubic function at x = 6?

• 12

• 8

• 4

• 0

Which interval does the square root function cover in the piecewise function?

• -2 < x <= 2

• 2 < x <= 6

• -2 <= x < 2

• 2 <= x < 6

Which interval does the cubic function cover in the piecewise function?

• -2 < x <= 2

• 2 < x <= 6

• -2 <= x < 2

• 2 <= x < 6

What is the correct piecewise function based on the analysis?

• sqrt(x) + 2 for -2 < x <= 2; x^3 + 4 for 2 < x <= 6

• x^2 + 2 for -2 < x <= 2; x^3 - 4 for 2 < x <= 6

• x + 2 for -2 < x <= 2; (x + 4)^3 for 2 < x <= 6

• sqrt(x + 2) for -2 < x <= 2; (x - 4)^3 for 2 < x <= 6