Math Is Fun Forum

With poly's its really easy: just look at the powers

All odd powers -> odd fcn

All odd powers -> odd fcn

All even powers -> even fcn

All even powers -> even fcn

YOu can do the graph yourself in your phone
Go to Google Play Store
In 'search' box enter 'Graphing calculator plus 84 83'
Install app to get TI-84 emulator on your phone
TI-84 can do things like find the minimum on a graph
(and there's lots of tutorials, how-to's, etc online for Texas Instruments TI-84)

1st part: Equilaterals have all sides the same length
so plug pairs of pts into Distance Formula
2nd part: Use Midpoint Formula to find midpts
Use Distance Formula to show all new sides have same length

just plug into midpoint formjula

Set the x and y coords equal

Solve for x and y

find 'v' for part A
plug that into the eqn they gave you
this is all they want for partt B

They gave you

They ask if the equation works with

So see if it works

Simplify
does this equal 10?

The only instrutions Im' seeing are the 3 quoted
sorry

domain: Look at where the graph goes from side to side
Does it quit (like with square roots) or have gaps (like with vert. asymps), or does it go everywhere?
Domain is wherever graph goes along x-axis
(not necessarily right next to the axis but you can trace up or down from the axis to the graph)

range: Look at where the graph goes from bottom to top
Does it quit (like with parabolas) or have gaps (like with hor. asymps), or does it go everywhere?
Range is wherever graph goes along y-axis
(not necessarily right next to the axis but you can trace right or left from the axis to the graph)

YOu can do graphing on your phone
Go to Google Play Store
In 'search' box enter 'Graphing calculator plus 84 83'
Install app to get TI-84 emulator on your phone
TI-84 can do things like find the minimum on a graph
(and there's lots of tutorials, how-to's, etc online for Texas Instruments TI-84)

Open google play store
Select 'search'
Enter 'carbon browser'
Select and install
Open carbon brwoser
Enter url for image that you uploaded
Long-press image (hold you finger on the image until a menu pops up)
Select 'open image in new tab'
Go to new tab
Press url box (it should look like i.imgur.io/[bunch of characters].webp?[query string]
note: [bunch of characters] in the new tab will NOT be the same as the [bunch of characters] in the original tab!!!
Select edit (pencil icon)
Erase (back-space) from the end until you get to the .webp
Replace .webp with .jpg
Select 'go' at bottom of keyboard
Your image should disply alone on the page
Copy new url and paste between [ img] [ /img] tags (without the extra spaces of course)

With your image from another thread i got this:

i.imgur.io/7uB3NEl_d.jpg

I removed the '_d' to get i.imgur.io/7uB3NEl.jpg

Putting it between the 'img' tags does this:

if you dont delete the underscore-d then you get a thumbnail (?) thats pretty small:

Plug x=1 into f and g
see which one gives you 3/5 for the answer

Plug x=4 into g
See what g(4) equals
This is y
Point on g is (4,g(4))

Domains are different for f and g
f: solve x+4=0; everything else is domain
g: solve x-2=0: everything else is domain

f: set (x^2 + 2)/(x + 4) = 1/2 and solve
g: set 2x/(x - 2), = 1 and solve

graph vertical asymptotes
use the rules to find horizontal asymptotes
plot intercepts
make T-chart
graph a bunch of other points
then draw graph

like Bob said: look at the graph for the range
(you already have the domains)

y-int: set x=0 and solve
x-int: set y=0 and solve

plug a+b in for each x in f
plug a-b in for each x in g
simplify if you can

f(0) comes from pt (0,3)
f(-6) comes from pt (-6,-3)

none of the pts has x=3
maybe f(-3)?
then use pt (-3,0)

f=0 comes from pts (-3,0),(6,0),(10,0)

f>0 comes from pts (0,3),(2,4),(4,3),(11,1)

use defs:
x-int: y=0, so pts (-3,0),(6,0)(10,0)
y-int: x=0, so pt (0,3)