Question

help! (5)/(x+4) average rate of change from 1 to x. so far i got this equation [(5)/(x+4)]-1(1/(x-1)

Answer 1

Is the question, if we have this function:
\[ y= \frac{5}{x+4} \]
what is its average rate of change between 1 and x ?

If so, you want to find the change in y divided by the change in x

when x= 1 y= 5/(1+4)= 5/5 =1
when x is x y = 5/(x+4)
the change in y is
\[ \frac{5}{x+4} - 1= \frac{5}{x+4}- \frac{(x+4)}{x+4} = \frac{5-x-4}{x+4}= \frac{1-x}{x+4}\]

the change in x is
x-1

the average rate is change in y divided by change in x
can you finish ?

Answer 2

is it x+4?

Answer 3

or 1/x+4

Answer 4

? /:

Answer 5

if im reading it correctly, the avg rate of change is the slope between f(x) and f(1)
\[\frac{f(x)-f(1)}{x-1}\]

Answer 6

it looks like phi determined that as well

Answer 7

yeah. so far i have (1-x)/(x+4) all over (x-1) but i don't know how to simplify. i think it's 1/x+4

Answer 8

\[\frac{a/b}{c}=\frac{a}{bc}\]

Answer 9

you can pull out a negative it seems to cancel like terms

Answer 10

\[\frac{(1-x)}{(x-1)(x+4)}\]
\[\frac{\cancel{(1-x)}}{-\cancel{(1-x)}(x+4)}\]
\[\frac{1}{-(x+4)}\]

Answer 11

thank you!

Answer 12

youre welcome