The value k that makes the piecewise function continous

The video tutorial explains the concept of discontinuity in a rational expression where X cannot equal zero. The teacher demonstrates how to simplify the expression by factoring out X, identifying the removable discontinuity, and evaluating the simplified expression. The tutorial also covers the graphical representation of the expression, highlighting the hole at X = 0 and explaining how to find the value that fills this hole.

What is the main reason X cannot be zero in the expression X^2/X?

• It causes a vertical asymptote.

• It results in a jump discontinuity.

• It leads to zero in the denominator.

• It makes the expression undefined everywhere.

What is the purpose of factoring in rational expressions?

• To change the domain of the expression.

• To increase the degree of the polynomial.

• To identify and remove discontinuities.

• To make the expression more complex.

What type of discontinuity is present in the expression after simplification?

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• Vertical asymptote

After simplifying the expression, what value can be plugged in for X to fill the hole?

• 0

• 1

• 3

• 2

What does the graph of the simplified expression look like?

• A line with a jump discontinuity

• A parabola with a hole at X = 0

• A line with a vertical asymptote

• A line with a hole at X = 0