Can anyone tell me what I'm doing wrong here?

Question

jh99 · Answer

attachment

campbell_st · Answer

Ok.. so if you factor the numerator you get 

$$y = \frac{(x -4)(x +1)}{(x - 4)}$$

so the equation can be simplified to 

$$x = x + 1$$

now look at the denominator x - 4   there is a discontinuity at x = 4

but since x - 4 is a common factor the discontinuity is a point rather than an asymptote

so the graph looks like 

|dw:1464676471395:dw|

the point of discontinuity means that at x = 4 the line doesn't exist

hope it helps

campbell_st · Answer

oops it should read 

the equation simplifies to

$$y = x + 1$$

campbell_st · Answer

the value x = 4 is substituted into the simplified version 

$$y = x + 1$$

jh99 · Answer

so... what did i do wrong in my graph??

campbell_st · Answer

well if you extend the  line  x = 4 up to where it intersects you line y = x + 1

the point of intersection is (4, 5) since x =4 is a discontinuity  or vertical asymptote

the point of intersection is a discontinuity

campbell_st · Answer

so have a look at my line|dw:1464677353255:dw|

so you didn't do a lot wrong... it was just identifying the type of discontinuity

jh99 · Answer

thank you. But how about the actual graph line?

jh99 · Answer

I need to find the domain and range for this as well....

campbell_st · Answer

well what value can't you have in the domain... 

and what value can't you have in the range... look at the graph...

campbell_st · Answer

well your dotted lin doesn't go through any of the points... 

here is my image of the graph... by putting the label on the point it hids the fact that they point (4, 5) should be an open circle...

jh99 · Answer

Oh thank you, I think I understand. You only used the equation x+1 right?

For the domain and range, 
I got...
Domain: (negative infinity, infinity), x does not equal to 4 
Range: All real numbers?!

skullpatrol · Answer

Should you exclude y=5 from your range?

jh99 · Answer

Shouldn't I exclude a specific point? (4,5)

I don't think the entire y axis of five should be excluded..? I'm not sure..

skullpatrol · Answer

The domain and the range are sets of allowed values, right?

jh99 · Answer

Yes

skullpatrol · Answer

Is a range value of 5 allowed?

jh99 · Answer

I don't know. I thought the range was all real values :o

skullpatrol · Answer

Except for 5.

jh99 · Answer

alright.. thank you :)

skullpatrol · Answer

That is what the "hole" in the line means :-)

jh99 · Answer

I see. "All real numbers" and "negative infinity to infinity" basically means the same thing right?