Question

Identify the graph of f(x) defined as indicated

Answer 1

How do you solve these? I've been having trouble with these all week.

Answer 2

Easiest way is probably to plot out some points in each of the 3 regions of the function

Answer 3

I mean like the function thing. I can't tell which graph is the right one :(

Answer 4

and then compare to the answer choices.

Give me a sec to look at the choices...

Answer 5

I think the whole "if x < 0" thing is throwing me off

Answer 6

The <, >, <=, => signs make me confused.

Answer 7

well, x<0 just means "for any x's that are less than zero"

Here, it's for x<-2, so the value of the function whenever x is less than -2 is the first of the 3 parts of the function definition. It should be a line of slope 2, but only for x values to the left of x = -2

Answer 8

For this one only, just to get you on the right track, I will just tell you it's (a), but knowing that, look at the function definition and then look at the 3 parts of the graph in (a), and you can find each part in the region of x values where it applies. So there's one line for x values less than -2, a different line for x values between -2 and 2, and a third line for x values greater than 2

Answer 9

So the part of these functions where it says whether x is less than or more than a given number, that sort of plots the points for you? Or like, plots them in a general area?

Answer 10

The function is just like a rule, but here it's a rule is different for different areas of x. A really easy comparison might be movie prices... kids are one price for ages (think "x values") less than 12, adults are a higher price for ages between 12 and 65, and seniors are less for ages above 65

Answer 11

So, yes, I think you have the right idea in general

Answer 12

By graph (a) are you talking about this graph?

Answer 13

An equation of a line is a function that is the same rule for all x values. These functions use different rules depending on what x values you are using

Answer 14

Or this one?

Answer 15

I'm trying to refer to the right one

Answer 16

yes, sorry... didn't think about the fact it wasn't labelled as (a). The first one

Answer 17

oh, wait!

Answer 18

:o

Answer 19

What is the symbol for the dark dot versus the white dot on the graphs?

Answer 20

If the sign is < or >, the dot is solid, it the dot it open, it's <=, or =>

Answer 21

I believe...

Answer 22

Right... so, it's actually the graph that ends in the number 25 in its name

Answer 23

the second, I think. I didn't pay close attention to the dots at first (my mistake!!)

Answer 24

It's alright, I had no idea anyways where to start! Lol. So are you talking about this graph? that ends in 25 for it's file name?

Answer 25

At x = -2, the function rule to use is the middle part, f(x) = 2x-2 because x=-2 falls into that area due to the <= and => in the rule. So you want to make sure the line starting there is a dark dot on both ends. The other two lines should have empty dots at x=-2 and x=2

Answer 26

That's the right graph in your last post

Answer 27

OHH okay, I'm kinda following you now (:

Answer 28

glad to help :)

Answer 29

Thank you so much for all your help!