Since any number, positive or negative, can appear as an exponent, the domain of the function is the set of all real numbers; in other words, is defined for all real values of . It is therefore impossible for the graph to have a vertical asymptote.

The horizontal asymptote of an exponential function can be found by noting that a positive number raised to any power must be positive. Therefore, and for all real values of . The graph will never crosst the line of the equatin , so this is the horizontal asymptote.

On the coordinate plane, a point with 0 as one of its coordinates lies on an axis.

On the coordinate plane, a point with a negative -coordinate and a positive -coordinate lies in the upper left quadrant - Quadrant II.

The vertical asymptote(s) of the graph of a rational function such as can be found by evaluating the zeroes of the denominator after the rational expression is reduced.

First, factor the numerator. It is a quadratic trinomial with lead term , so look to factor

by using the grouping technique. We try finding two integers whose sum is and whose product is ; with some trial and error we find that these are and , so:

Break the linear term:

Regroup:

Factor the GCF twice:

Therefore, can be rewritten as

Cancel the common factor from both halves; the function can be rewritten as

Set the denominator equal to 0 and solve for :

The graph of therefore has one vertical asymptotes, the line of the equations . The line of the equation is not a vertical asymptote.

The vertical asymptote(s) of the graph of a rational function such as can be found by evaluating the zeroes of the denominator after the rational expression is reduced.

First, factor the denominator. It is a quadratic trinomial with lead term , so look to "reverse-FOIL" it as

by finding two integers with sum 6 and product 5. By trial and error, these integers can be found to be 1 and 5, so

Therefore, can be rewritten as

Set the denominator equal to 0 and solve for :

By the Zero Factor Principle,

or

Therefore, the binomial factor can be cancelled, and the function can be rewritten as

If , then , so the denominator has only this one zero, and the only vertical asymptote is the line of the equation .

The radius of a circle with area can be found as follows:

The circle, the central angle, and the chord are shown below:

By way of the Isosceles Triangle Theorem, can be proved equilateral, so , the correct response.

The domain of any polynomial function, such as , is the set of real numbers, as a polynomial can be evaluated for any real value of .

If we graphed the given complex number on a set of real-imaginary axes, we would plot the real value of the complex number as the x coordinate, and the imaginary value of the complex number as the y coordinate. Because the given complex number is as follows:

We are essentially doing the same as plotting the point on a set of Cartesian axes. We move units right in the x direction, and units down in the y direction, which puts us in the fourth quadrant, or in terms of Roman numerals: