Limits and Discontinuities in Piecewise Functions

The video tutorial focuses on graphing piecewise functions, identifying their domain and range, and analyzing limits and continuity. It covers graphing x^2 and linear functions, identifying discontinuities, and understanding the domain and range. The tutorial also explores limits and end behavior, graphing 1/x and radical functions, and concludes with a final example summarizing key concepts.

What type of discontinuity is present at x = 0 in the first piecewise function?

• Infinite discontinuity

• Point discontinuity

• Removable discontinuity

• Jump discontinuity

What is the domain of the first piecewise function?

• (-∞, 0) ∪ (0, ∞)

• (-∞, ∞)

• (-∞, 0] ∪ [0, ∞)

• [0, ∞)

As x approaches negative infinity, what does the function f(x) approach in the first piecewise function?

• 0

• -∞

• ∞

• 1

What is the limit of f(x) as x approaches 0 from the right in the first piecewise function?

• 0

• -2

• 2

• Does not exist

What is the domain of the second piecewise function involving 1/x and √x?

• (-∞, 0) ∪ (1, ∞)

• (-∞, ∞)

• (-∞, 1) ∪ (1, ∞)

• (0, 1) ∪ (1, ∞)

What type of discontinuity is present at x = 0 in the second piecewise function?

• Removable discontinuity

• Infinite discontinuity

• Jump discontinuity

• Point discontinuity

As x approaches infinity, what does the function f(x) approach in the second piecewise function?

• ∞

• 1

• -∞

• 0

What is the range of the final piecewise function involving absolute value and linear components?

• (-∞, 0) ∪ (0, ∞)

• (-∞, 3) ∪ (3, ∞)

• (-3, 0) ∪ (0, ∞)

• [-3, 0) ∪ (0, ∞)

What type of discontinuity is present at x = 4 in the final piecewise function?

• Jump discontinuity

• Point discontinuity

• Removable discontinuity

• Infinite discontinuity

What is the limit of f(x) as x approaches 4 from the left in the final piecewise function?

• 0

• 3

• Does not exist

• 4