Discontinuous Piecewise Functions

What type of discontinuity is characterized by a sudden change in the value of a function?

• Horizontal asymptote

• Hole

• Jump discontinuity

• Vertical asymptote

In the first example, what is the domain of the function y = E^x for x > 0?

• (-∞, ∞)

• [0, ∞)

• (0, ∞)

• (-∞, 0)

What is the range of the function y = 1/x for x < 0?

• (-∞, 0)

• (0, ∞)

• [0, ∞)

• (-∞, ∞)

How does reflecting a logarithmic graph about the Y-axis affect its domain?

• The domain becomes all real numbers

• The domain remains unchanged

• The domain becomes all negative values

• The domain becomes all positive values

What transformation is applied to the cubic graph in the second example?

• Reflection about the X-axis

• Horizontal shift

• Vertical shift

• Reflection about the Y-axis

In the third example, what is the effect of a vertical shift on the square root function?

• It changes the domain

• It changes the range

• It changes both domain and range

• It has no effect

What is the domain of the quadratic function with a vertical shift in the third example?

• [0, ∞)

• (0, ∞)

• (-∞, 0)

• (-∞, ∞)

In the final example, what is the effect of a vertical shift on the absolute value function?

• It changes the range

• It changes the vertex position

• It changes the slope

• It changes the domain

What is the range of the absolute value function after the vertical shift in the final example?

• [1, ∞)

• (-∞, ∞)

• (-∞, -4)

• (-4, ∞)

Which of the following is not a type of discontinuity discussed in the video?

• Jump

• Hole

• Vertical asymptote

• Horizontal asymptote