Question

I need some serious help please :(..
Make a summary table with these headings shown for each graph: Interval, Sign of Function, Sign of Slope, Change in Slope
I dont know how to figure out these??

Answer 1

this is the graph i got with the question : pic.twitter.com/7aVfNYi4

Answer 2

here, can u see this?

Answer 3

Interval Table
X Y
-4 close to zero
-2 0.2
0 1
0.5 2
1 Infinity
2 1
3 0.2

Answer 4

at the back of the book, the intervals are x<1 and x>1

Answer 5

i understand the intervals, but not the rest of them like sign of slope..

Answer 6

sign of functions
f(x)= infinity, if x=1
f(x)=1 to infinity, if interval is from 0<x<1
f(x)=infinity to 1, if interval is from1<x<2
f(x)=1 to approach zero, if interval is from x>2
f(x)=1 to approach zero, if interval is from x<-2

Answer 7

where did you get 0.25 and 0.2 from?

Answer 8

sign of slope and change of slope
y2- y1
slope m=-------
x2 - x1
from interval [-2,-1], f(-2)=0.2 , f(-1)=0.25 therefore

0.25-0.2 0.05 0.05
m1=-----------=--------= --------= 0.05 positive slope here
-1-(-2) -1+2 1

from interval [-1,0], f(-1)=0.25 f(0)=1

0.25-1 -0.75
m2=---------=-----------= +0.375 still positive here
-1-1 -2

the slope here is increasing from positive 0.05 to 0.375

Answer 9

look at the graph
x=-1, y=f(-1)=0.25
x=-2, y=f(-2)=0.2

Answer 10

those are only approximation and assumption only to be able to know if you are on positive or negative slope changing decreasing or increasing

Answer 11

but if the sign is change from positive to negative it is decreasing function
and from negative to positive sign it is increasing functon

Answer 12

ohhh it makes sense!! and then you do the same thing to the other side right, because what you did was x<1 (for slope) and then I do x>1 ?

Answer 13

next try that from interval [2,1] or from x=2 and x=1
find f(2)=? , and f(1)=? then find out if it is increasing or dec

Answer 14

yeah......try that

Answer 15

okay so f(2)=1 and f(3)=0.25

Slope= 0.25 - 1 / (3-2)
= -0.75

f(3)= 0.25 f(4)= 0.02

slope= 0.02-0.25 / (4-3)
=-0.23

Negative and decreasing!!! :D

Answer 16

Thank you so much!!

Answer 17

yessssss....good luck now and enjoy lol :D

Answer 18

YW