Squaring an expression, then squaring the result, amounts to taking the original expression to the fourth power. Therefore, we can first square : 

Now square this result:

For any expression , . That is, we can raise an expression to the power of eight by squaring it, then squaring the result, then squaring that result. 

First, we square:

Square this result to obtain the fourth power:

Square this result to obtain the eighth power:

The vertical asymptote is , where  is found by setting the denominator equal to 0 and solving for :

This is the equation of the vertical asymptote.

Set  in the equation and solve for .

This is impossible, so the equation has no solution. Therefore, the graph has no -intercept. 

Set  in the equation and solve for .

The -intercept is 

To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by :

As  approaches positive or negative infinity,  and  both approach 0. Therefore,  approaches , making the horizontal asymptote the line of the equation  .

Set  in the equation:

The -intercept is .

First, we determine the equation of the boundary line. This line includes points  and  , so the slope can be calculated as follows:

We can find the slope-intercept form of the line by substituting  

in the following equation:

The equation of the boundary line is .

The boundary is excluded, as is indicated by the line being dashed, so the equality symbol is replaced by either  or . To find out which one, we can test a point in the solution set - for ease, we will choose :

 _____   

  _____ 

  _____ 

0 is greater than  so the correct symbol is . 

The correct choice is .

First, consider the characteristics of the line. The slope is equal to 2 and the y-intercept is equal to 3. Because the line is solid, that indicates that the inequality is "greater than or equal to" or "less than or equal to". Finally, choose a point to determine the direction of the shading. The origin (0,0) is usually a good choice unless it falls on the line. If the chosen point makes the statement true, it must be included in the shaded region. If it is false, it must not.

Because 0 is less than 3 and the origin is not included in the shaded region, the correct answer must include "greater than or equal to"

In order to graph the inequality pictured above, we must first find the equation of its boundary line. Based on the image, we see that the line includes the points  and , so the slope of the line is

.

We can now find the -intercept form of the line by substituting  and the point   into the slope-intercept equation  and solving for :

The equation of the boundary line is therefore . Since we see that the boundary line is dashed, we know that the values on the line are excluded from the inequality, so the  sign will be replaced by a  or a .

In order to determine which one, we can test a point in the solution set; let's test  since it's the simplest to substitute:

 _____

 _____

 _____

, so the correct symbol is :