Question

Help with two graphing questions?

Answer 1

Piecewise function graph

2. Determine the graph of the function: f(x)= 2x if x < -2
2x-2 if -2 is less than or equal to x is less than or equal to 2
-2 if x >2

Answer 2

@jim_thompson5910 @jimmyao98

Answer 3

@satellite73 @phi @ganeshie8

Answer 4

to graph this, you simply graph each piece on the same coordinate axis

Answer 5

but keep the restrictions in mind

Answer 6

so for instance, you start with graphing y = 2x

but you only graph it for x values less than -2

Answer 7

would it be this graph with the blue circle next to it?

Answer 8

there's a slight issue with that choice

hint: look at the endpoints (and note the open/closed circles)

Answer 9

okay so i'm going to say it's either this first one

Answer 10

or this third one (the one at the top)

Answer 11

You can tackle this problem this way.

for the first line
f(x)= 2x if x < -2
this goes up to but does not reach x=-2
the < means you should put an open circle at f(-2)

f(-2) using the first line is 2*-2 = -4. So you should look for an open circle at (-2,-4)
Can you find any graphs that have an open circle at that point ?

Answer 12

yes the most recent picture i posted has open circles there

Answer 13

If there is only one choice with an open circle, that will be the answer. But there might be more than one choice that works, in which case we look at some of the other lines.

Which choices can you definitely rule out ?

Answer 14

choices 1 and 2 because they don't have open circles where they should

Answer 15

so right now you have a 50-50 chance.

but let's look at the last line
f(x) = -2 if x >2

First does the > mean an open circle or a solid circle ?

Answer 16

solid circle

Answer 17

Pay attention... x>2 means x can be very very very close to 2, but it is not allowed to be 2
we show this by using an open circle

if we had x≥2 then x can be 2 or bigger. we use a solid circle if x is allowed to be 2

so


f(x) = -2 if x >2

First does the > mean an open circle or a solid circle ?

Answer 18

open circle then?

Answer 19

yes, open circle. the = part of >= (or ≥) means solid. just > or < means open

f(x) = -2 if x >2
now at x=2 what is f(x) ? f(2)= -2 (but with an open circle)
look for a graph that has an open circle at (2,-2)

Answer 20

it's the one i chose :) can i have help with 1 more?

Answer 21

I can't tell which one you chose. Can you repost it?

Answer 22

sure

Answer 23

yes, that is good

Answer 24

awesome! can i have help with 1 more? @phi

Answer 25

can you make this a new post please ?

Answer 26

sure