The simplest way to solve this problem is to plug all of the answer choices into the provided equation, and see which one results in a power of  .  

Alternatively, one could set up the equation,

  and factor, use the quadratic equation, or graph this on a calculator to find the root. 

If we were to factor we would look for factors of c that when added together give us the value in b when we are in the form,

.

In our case . So we need factors of  that when added together give us .

Thus the following factoring would solve this problem.

Then set each binomial equal to zero and solve for v.

Since we can't have a negative power our answer is .

The  inside the argument has the effect of shifting the graph  units to the left. This can be easily seen by graphing both the original and modified functions on a graphing calculator.  

To answer this question, we need to correctly identify where to plug in our given values and solve for .

Points on a graph are written in coordinate pairs. These pairs show the  value first and the  value second. So, for this data:

 means that  is the  value and  is the  value.

We must now plug in our  and  values into the original equation and solve. Therefore:

We can now begin to solve for  by adding up the right side and dividing the entire equation by .

Therefore, the value of  is .

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 .

Because points on a graph are written in the form of , and the point given was , this means that  and .

In order to solve for , these values for  and  must be plugged into the given equation. This gives us the following:

We then solve the equation by finding the value of the right side, then dividing the entire equation by 5, as follows:

Therefore, the value of  is .

A line is an asymptote in a graph if the graph of the function nears the line as X or Y gets larger in absolute value.  

The graph has x-intercepts at x = 0 and x = 8. This indicates that 0 and 8 are roots of the function.

The function must take the form y = x(x - 8) in order for these roots to be true.

The parabola opens downward, indicating a negative leading coefficient. Expand the equation to get our answer.

y = -x(x - 8)

y = -x² + 8x

y = 8x - x²

Therefore, the answer must be y = 8x - x²

The denominator cannot be zero, otherwise the function is indefinite. Therefore x cannot be –2 or –3.

One of the properties of taking an absolute value of a function is that the values are all made positive. The values themselves do not change; only their signs do. In this graph, none of the y-values are negative, so none of them would change. Thus the two graphs should be identical.