Question

anyone know what dividing ln(x)/(x) does exactly to the graph? so the function is y=ln(x)/(x). I'm supposed to explain how "each algebraic piece of the function affects portions of the graph" so the algebraic piece in this case is the division of x.

Answer 1

Graph them individually in a calculator, you would see that the ln x dominates and bends the x

Answer 2

oh okay wait are you still here? can we discuss this more?

Answer 3

can you be more specific about it "bends the x" and we need to talk specific portions of the graph so when x < 0 and when x>0 what happens i think

Answer 4

I'll have do look this up, see if i have any info in old notes.

Answer 5

okay thanks!

Answer 6

:)

Answer 7

find anything? :)

Answer 8

You have to plug in x values it would give you clues. X values less than zero undefined and negative denominator x --> tends to zero. Do same process other direction.

Answer 9

wait let me see if I understand so when x < 0 all values are undefined, when x > 0 though..

Answer 10

All ln values, the denominator is defined.

Answer 11

when x < 0 on my calculator's table it just says ERROR

Answer 12

Yes, laws of log. Log equal to or greater than zero

Answer 13

it looks like after a certain point it pulls the graph down and keeps it close to the x axis compared to just plain y=ln(x)

Answer 14

Effect of smaller ln x values divided by larger x values in denominator.

Answer 15

right, ok now im going to type my teacher's example she gave us and we can try to mimick she explained for y=e^(x)+x that when x < 0 the graph of the function is closer to the x part of the function. This is because as x gets more and more negative, e^(x) gets smaller and samller and the function gets closer to x. When x>0 the graph is closer to the e^(x) [art f the function because as x approaches inifinity, e^(x) becomes much larger than x so the graph acts like the e^(x) part.

Answer 16

Best explanation, I can think of, on the bottom half of the graph it tends to zero because ln x can not be less than zero, points downward due to negative numbers in denominator.
Top half, very small values of x divided by very large values of x tends to zero along the y axis to positive infinity.

Answer 17

oh okayyy

Answer 18

still there?