Is this even possible?

Question

1.     For the function g(x)=1/x-4+2
Write the equations of the asymptotes and label them on the coordinate plane.
Enter at least five values in the table of values.
Graph the function on the coordinate plane.

 

Answer 1

g(x) = 1/(x-4) + 2

 

There is a vertical asymptote at x = 4.  Why?  Because at x=4, the fraction 1/(x-4) = 1/(4-4) = 1/0, which is undefined.

 

There is a horizontal asymptote at y=2 because when x gets very large, 1/(x-4) --> 0 and g(x) --> 2.

 

g(x) is a function transformation of f(x) = 1/x.  The -4 shifts the graph 4 units to the right along the x-axis.  The +2 shifts the graph up two units on the y-axis.  Here are a few values:

 

 x     y  

 0   7/4    (the graph crosses the y-axis here)

 1   5/3

-1   9/5

 

You can fill in a few more. You can view the graph of g(x) at the link below:

 

http://www.wyzant.com/resources/files/302880/graph_of_g_x_1_x_4_2