Find the Vertical and horizontal asymptotes, then find the Domain and Range of the function

Question

h(x) = 2 -3

x-4

Answer 1

Hi Shaun I'm Eddie I can help today. I'm not sure if this is the exact problem but let me know.

2 - 3

x-3

Asymptopes come in two forms 1/0 or negative square root. Always look for 1/x type for these problems.

1/0 is undefined so it cannot reach it.

Look up a general graph of 1/x very important for this explanation? From the left small negative fractions approach 0. On y-axis is the undefined point where from the left it approaches negative infinity and the right positive infinity. Towards right also approaches zero.

Do you see a vertical asymptote? x =0 or y-axis

Do you see the horizontal asymptote? y = 0 or x-axis

Why well no matter how small x is 1/x always a fraction not quite 0.

But for your problem the asymptomes are shifted. Looking 2/(x-3) can you tell by how much well simply the opposite it says -3 but it's actually +3 shift or to the right.

Now the confusing part is -3 on the outside also is a shift but this time no opposite so -3 is the shift 3 down.

Lastly the 2x means you double the y values make the graph slope steeper. Start by using the new info. If the picture above is shifted 3 right then simply move (0,0) see where graph asymptotes intersect to (3,0). However we also moved down 3 so (3,-3) is correct new intersection draw dashed lines from this point.

The new asymptotes is 3 = x and y= -3. Now plug in a few points around the (3, -3) so I recommend 2, 2.5, 3.5, 4 draw the graph as seen with the line approaching infinity faster and 0 faster. If you like further assistance feel free to reach out for a first free session ok.