Removable Discontinuity Vocabulary

What is a removable discontinuity?

• A point on the graph where the slope is zero.

• A point on the graph of a rational function where the function is undefined, but the discontinuity can be 'removed' by simplifying the function.

• A point where the graph intersects the x-axis.

• A point where the function's value approaches infinity as x approaches a specific value.

For f(x), x = 2 would be defined as...

• a removable discontinuity

• a vertical asymptote

• a rational function

• a removable factor

Vertical Asymptote

• A vertical line that the graph crosses when the denominator equals zero.

• A point on the graph where the graph intersects the x-axis.

• A vertical line that the graph of the function approaches but never touches, caused by a non-cancelled factor in the denominator.

• A point where the numerator equals zero.

A vertical asymptote is

• A point where the function's value is undefined.

• A horizontal line that the graph approaches as x approaches infinity.

• A vertical line where the function approaches infinity or negative infinity.

• A point where the graph crosses the x-axis.

Zero of a Function

• A vertical asymptote where the graph crosses the x-axis.

• A point where the function approaches infinity.

• The x-value where the numerator of the rational function equals zero, making the function’s value zero.

• A point on the graph where the denominator equals zero.

What is the difference of squares defined as?

• A mathematical expression where two terms are added together.

• A rule used when the factor can be simplified using square roots.

• A rule for multiplying two binomials.

• A process to find the sum of two squares.

Factorable Form

• The function is written as a sum of fractions.

• The function is written as a product of terms that cancel out.

• The function has a constant term and no variables.

• The function is an exponential equation.

Simplified Rational Function

• A function that is undefined at every point.

• A function that only has vertical asymptotes.

• A function that has no horizontal asymptotes.

• A function that has no removable discontinuities after canceling common factors.