To find an oblique asymptote of a rational function whose numerator has higher degree than its denominator, as is the case here, divide the former by the latter, as follows:

Note that "missing" terms have been inserted in the dividend as terms with zero coefficients.

Divide the leading term of the dividend by that of the divisor:

Place this in the quotient, and multiply this by the divisor:

Subtract this from the dividend. The figure should look like this:

Repeat with the difference:

The figure now looks like this:

The difference has degree less than that of the divisor, so the division is finished. The equation of the oblique asymptote of the graph of  is taken from the quotient, and is the line of the equation .

The -intercept of the graph of  is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for  in the definition:

The -intercept(s) of the graph of  are the point(s) at which it intersects the -axis. The -coordinate of each is 0; their -coordinate(s) are those value(s) of  for which , so set up, and solve for , the equation:

Square both sides to eliminate the radical:

Add 9 to both sides:

,

the correct choice.

To find the range of the function , it is necessary to note that, regardkess of the value of , 

Add 25 to both sides, then take the positive square root:

It follows that

,

and that the correct range is  .

This question relies on both the vertical-line test and the definition of a function. We need to use the vertical-line test to determine which of the graphs is not a function (i.e. the graph that has more than one output for a given input). The vertical-line test states that a graph represents a function when a vertical line can be drawn at every point in the graph and only intersect it at one point; thus, if a vertical line is drawn in a graph and it intersects that graph at more than one point, then the graph is not a function. The circle is the only answer choice that fails the vertical-line test, and so it is not a function.

Complex numbers can be represented on the coordinate plane by mapping the real part to the x-axis and the imaginary part to the y-axis.  For example, the expression  can be represented graphically by the point .

Here, we are given the graph and asked to write the corresponding expression.

 not only correctly identifies the x-coordinate with the real part and the y-coordinate with the imaginary part of the complex number, it also includes the necessary . 

 correctly identifies the x-coordinate with the real part and the y-coordinate with the imaginary part of the complex number, but fails to include the necessary .

 misidentifies the y-coordinate with the real part and the x-coordinate with the imaginary part of the complex number.

 misidentifies the y-coordinate with the real part and the x-coordinate with the imaginary part of the complex number.  It also fails to include the necessary .

Complex numbers can be represented on the coordinate plane by mapping the real part to the x-axis and the imaginary part to the y-axis.  For example, the expression  can be represented graphically by the point .

Here, we are given the complex number  and asked to graph it.  We will represent the real part, , on the x-axis, and the imaginary part, , on the y-axis.  Note that the coefficient of  is ; this is what we will graph on the y-axis.  The correct coordinates are .

The -coordinate(s) of the -intercept(s) are the real solution(s) to the equation . We can use the quadratic formula to find any solutions, setting  - the coefficients of the expression.

An examination of the discriminant , however, proves this unnecessary.

The discriminant being negative, there are no real solutions, so the parabola has no  -intercepts.

When plotting a complex number, we use a set of real-imaginary axes in which the x-axis is represented by the real component of the complex number, and the y-axis is represented by the imaginary component of the complex number. The real component is    and the imaginary component is  ,  so this is the equivalent of plotting the point    on a set of Cartesian axes.  Plotting the complex number on a set of real-imaginary axes, we move    to the left in the x-direction and    up in the y-direction, which puts us in the second quadrant, or in terms of Roman numerals:

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: