Polynomial and Rational Functions

Undefined

Negative two

Zero

Eight

Exclusively if m is an integer.

Any real number except zero.

None; the equation always has an horizontal asymptote at y=q.

Only when m is greater than one.

Add both numerator and denominator together set equal to zero then solve for x.

Set denominator equal to zero and solve for x.

Set numerator equal to zero and solve for x.

Multiply both numerator by denominator set equal to zero then solve for X.

x = 0

y = 6

x = 6

y = 0

The graph crosses over itself.

The graph approaches an undefined value along a vertical line.

The graph makes a sharp turn.

The graph stretches towards negative infinity horizontally.

y = 3

x = -4

y = -4

x = 3

60 degrees

45 degrees

120 degrees

90 degrees

Both paths are equal because both objects have consistent speeds and distances covered are equal.

Interval of object with a longer path due to a greater numerator affecting altitude.

Interval of object with a shorter path since it has a larger denominator influencing the steepness of the curve.

Both objects travel at the same pace, thus the identical intervals are covered.

Any unique solution where $2b \neq 1$.

B must exactly equal one half.

B must not equal one half in order to create discontinuities.

There are no such values for which $g(B)$ is continuous.

The numerator and denominator have the same roots

The numerator has no real roots

The denominator has no real roots

The denominator has exactly one real root