Functions and Limits
Hi can you check if these answers are correct?
1. Sketch the graph of a function that satisfies these conditions:
limf(x) = 2
lim f(x) = 0
f(0) = 2
f(4) = 1
Does this give me the these points?
(0,2) approaching from the left
(0,0) approaching from the right
(4,3) approaching from the left
(4,0) approaching from the right
Also, since I have the point (0,2) twice, is there anything special I need to do with it?
2. Determine the infinite limit
lim (x2 + 1) / (x2 - 4x + 4)
= (x(x-2)) / (x-2)(x-2)
= x / (x-2)
=2 / 0 = positive infinity
3. Graph this function
y=(x2+1) / (3x-2x2)
How do i graph this without using a calculator?
Re: Functions and Limits
For (1), you need a "solid dot" at (0,2) and an "open circle" at (0,0). Similarly, you need a "solid dot" at (4,1) and "open circles" at (4,0) and (4,3).
In problem (2) you factored to get , which is incorrect. You only need to factor the denominator to get . The answer is still .
For (3), has two zeros, which will be vertical asymptotes of the function. As x goes to or , y goes to . Beyond that, I think you might have to calculate a few points. A graphing calculator or graphing tool on the computer is good for checking your work.