Question

Which inequality matches the graph below? (Graph Attached)

Answer 1

Choices:
y > |x + 2| + 1

y < |x – 2| + 1

y < |x + 2| – 1

y > |x – 2| – 1

Answer 2

Well, what kind of functions act like that when graphed?

Answer 3

lol nvm....all the answer choices show that it is an absolute value function lol....so how would you go about solving this?

Answer 4

I've been trying to find that out, i don't have any examples in my notes :/

Answer 5

Well we can begin to eliminate 2 of the answers...is this a GREATER THAN function...or a LESS THAN function?

Answer 6

How do i determine that?

Answer 7

The easiest way is...look at the graph....is the point (0,0) in the shaded area?

Answer 8

Yes

Answer 9

So you can take one of each (Greater than, less than) equations in your answer choices....and plug in 0 for 'y' a 0 for 'x'

so lets look at answer choices A and B

y > |x + 2| + 1
0 > |0 + 2| + 1
0 > |2| + 1
0 > 3
NO....this is NOT a GREATER THAN function

y < |x – 2| + 1
0 < |0 - 2| + 1
0 < |-2| + 1
0 < 2 + 1
0 < 3
YES....this IS a LESS THAN function

So...now you can eliminate answer choices A and D right?

Answer 10

So if the origin of the graph is in the shaded area then it is a less than function?

Answer 11

@johnweldon1993 ?

Answer 12

not in all examples no...don't make that assumption.....just a way to check.

so now...

if you add a 1 to a function...that shifts the graph UP above the origin by 1 correct? ...well this is BELOW the origin...so it must be subtracting 1...what choice are we left with?

Answer 13

B?

Answer 14

no B is the one where you add 1 to a function....here I'll do a visual for you ...makes it easier to understand

Answer 15

now if you add 1 to that function....you move that graph UP 1 unit ...

if you SUBTRACT 1 from that function....you move that graph DOWN 1 unit.....the answer would be C right?

Answer 16

Ah yes, i understand now. Visuals help lol

Answer 17

haha no problem!

Answer 18

Can i ask if i have gotten this right?

Answer 19

I got

Answer 20

@johnweldon1993

Answer 21

Can I guess that 1 of the answer choices is

\[x ^{13/5}\]

Answer 22

The choices are:

x 1/5

x 14/15

x 1/2

x 5/9

@johnweldon1993

Answer 23

Nvm those are the wrong ones.

Answer 24

There is a 13/5 though.

Answer 25

lol I was just going to say...that's very odd haha....when you multiply exponents with the same bases......you add the exponents

Answer 26

I'm curious as to how you got 6/5 however...can you show me what you did?

Answer 27

I simplified the fractions. So 12 went to 6 and 10 went to 5 :p

Answer 28

\[x ^{3/5} x ^{4/2}\]

this becomes

\[x ^{\frac{ 3 }{ 5 } + \frac{ 4 }{ 2 }}\]

from there you find the least common denominator which is 10 here

so

6 20
-- + ---
10 10

26
---
10

simplify that into

13
---
5

and raise 'x' to that power

x ^ (13/5) :)

Answer 29

Thanks again!