Question

Can someone Check my answer?

What is the domain of the function f(x) = x2 + 5?

Answer 1

I chose the last one.

Answer 2

What is the range of the function f(x) = x2 + 5?

Answer 3

^^I chose the third one^^

Answer 4

the domain are all the x values that are "legal" in the function.
There is no number that "causes trouble" : e.g. 1) divide by 0, 2) sqrt of a negative number
in other words, all real numbers are ok for the domain

Answer 5

***What is the range of the function f(x) = x2 + 5?****
the range are all the numbers that f(x) can be

notice that x^2 means x*x
if x is negative: example x=-1, we would get -1*-1= 1 (a POSITIVE number)
in other words, all numbers for x , after being squared , are positive.
the smallest x^2 we can get is 0*0= 0
so the smallest f(x) can be is 0+5 = 5
Can you try again?

Answer 6

Okay, give me a few so I can think this over. THANK YOU SO MUCH

Answer 7

Quick question, what does the "R" mean?

Answer 8

the script R is short for "all real numbers"

Answer 9

Okay so for the first one, it is the "R" one, correct?

Answer 10

yes

Answer 11

I think the second one is real numbers, right?

Answer 12

the range is not all real numbers.

if you have x^2 + 5
how would you get , for example, 0 ?
no matter what x you use, you won't get 0 out (for the reason I posted up above)

Answer 13

Okay, so the targeted number is zero?

Answer 14

do you see how if x is 0, you get 0*0+ 5 or just 5 ?
if x is bigger than 0 you get something bigger than 5
if x is less than 0, after you square it, it becomes positive, and you add this to 5... making the answer bigger than 5.

Answer 15

**Okay, so the targeted number is zero? ***
no. zero was just an example of a real number that you can't get, using the expression
x*x + 5

Answer 16

I am not sure if zero or 5 is the best answer.

Answer 17

I am really sorry. I am really confused. Thank you for your patience.

Answer 18

you are given
f(x) = x*x+ 5

and are asked, what numbers can f(x) be? (i.e. what is the range of f(x) )

I am trying to show that the *smallest* f(x) can be is 5 (when x is 0)

you can test a few x values:
-1, 0, +1
you will get out
-1 --> 6
0 --> 5
1 --> 6
and it should be clear that as x gets big, what you get out also gets big
(any number we want... but we can never get smaller than 5)

Answer 19

Yes, I can see you are missing some idea. If you can explain what is confusing, maybe we can figure out what idea you need to learn.

Answer 20

I am not sure what number I am trying to get for the question. What you explain seems easy but in a way not as 'straight' as I would like to put it.

Answer 21

*** What is the range of the function f(x) = x2 + 5?***

The first idea is this: you are given a "rule" to "find numbers"
The rule says:
pick a number (in this case any real number)
multiply it by itself
add 5

the number we get is the "new number" and we call it f(x)

the question
*** What is the range***
is asking, "what numbers can f(x) be?"

ok so far?

Answer 22

Yeah, so far so good!

Answer 23

to find what numbers f(x) can be, we could do this:

try all possible x values, and see what f(x) numbers we get out.

that is a lot of work.... but we can use common sense.

Let's think of just positive x numbers, from 0 to infinity

as we make x bigger, the rule
f(x) =x*x+5
gives us new numbers

what number is f(x) when x is 0 ?

Answer 24

do you know how to find f(x) when x is zero ?

Answer 25

No

Answer 26

The rule says:
pick a number (in this case we are doing zero)
multiply it by itself
add 5

Answer 27

Okay for -5 it would be 25+5=30

Answer 28

yes. but let's just do x=0

Answer 29

Okay. so it would be five.

Answer 30

yes. and for x=1 ?

Answer 31

6.

Answer 32

and say we picked x= 0.5 (x= 1/2)

Answer 33

0.5*0.5 = 0.25 (or 1/2 * 1/2 = 1/4 which is 0.25)
then add +5

x= 1/2 gives us 5.25

Answer 34

Okay, so far so good!

Answer 35

The idea is as x gets bigger, we can get *any* number out that is 5 or bigger

does that make sense?

Answer 36

Yeah!

Answer 37

now think about it. at x=0 we get out 5
for x bigger than 0, we do x*x (to get a number bigger than 0) and when we add 5, we get a number bigger than 5

so I expect that we can get numbers out from 5 up to whatever you want.

what about if x is negative ?? i.e. x is less than zero?

Answer 38

for example, what do we get for x= -1

Answer 39

use the rule:
-1 * -1 + 5
1+5
6

we get out 6

ok ?

Answer 40

Yeah, makes sense!

Answer 41

if x is negative, and we multiply it by itself, we get a positive number
(because a minus times a minus is plus)
then we add 5

it looks like as x gets more and more negative, f(x) gets bigger and bigger

ok?

Answer 42

Okay.

Answer 43

so it looks like the "range" is 5 or bigger

Answer 44

the allowed x numbers (i.e. we call it the domain) are all real numbers
which means negative numbers, zero, and positive numbers.
we figured out that for all these x's, the rule
x*x + 5
can never be smaller than 5
but it can be as big as we want (by picking a big enough x)

Answer 45

Oh, wait, I think I hear the hamster turning the wheel in my head. I am sure the answer is D because it is adding positive five. So the X has to equal five or bigger...

Answer 46

to write down the answer for the range we use
\[ f(x) \ge 5 \]
we put the f(x) next to the "big end" of > and the 5 next to the "small end" of >

Answer 47

don't confuse x with f(x)
x is what we put in (to the rule)
f(x) is the new number we get out.
we are figuring out what f(x) "ranges over"

Answer 48

The reason we learn this stuff is for when we learn about inverse functions.

Answer 49

Oh.. got it.

Answer 50

one of the reasons people are taught math is because it makes the hamster work hard. It needs exercise.

Answer 51

Yeah, mine is out of shape when it comes to math.