Question

Which of the following functions have a domain of (-infinity, infinity), and a range of (2, infinity)?
Check all that apply
A. f(x)= 3^x+2
B. f(x_= 3^x-2
C. f(x)= 0.25^x +2
D. f(x)= 0.25^x-2

Answer 1

how far did you get here?

Answer 2

well honestly i have a hard time with problems like these i always guess could you explain how to start ?

Answer 3

what is the domain in general? What does the term mean?

Answer 4

If you had to define it in your own words, what would you say?

Answer 5

domain means all the x terms or the independent variable

Answer 6

basically all of the allowed inputs of a function

Answer 7

for something like f(x)= 3^x+2, are there any restrictions on x?

Answer 8

no i do not think so

Answer 9

you are correct, there are no restrictions

you can plug in ANY real number for x and get some output

Answer 10

so that's why the domain of f(x)= 3^x+2 is (-infinity, infinity)

Answer 11

when you mean restrictions does that mean it equals zero?

Answer 12

the same logic/reasoning applies to the other answer choices as well

Answer 13

well by "restrictions" i mean values of x that are not allowed

for example, the function \(\Large f(x) = \frac{1}{x-1}\) has the restriction that \(\Large x \neq 1\) because x = 1 makes the denominator 0 (and you can't divide by zero)

Answer 14

ok and so when there are no x value restrictions the domain will always be (-infintity, infinity)?

Answer 15

exactly

Answer 16

so far, all choices are the answer

but...we've yet to look at the range

Answer 17

right and the range is all the output values

Answer 18

all the possible output values, yes

Answer 19

what is the range of the first answer choice?

Answer 20

(2, infinity) since there is a positive 2 meaning as 2 approached infinity

Answer 21

correct, the range of 3^x is (0,infinity)

the +2 shifts up the range 2 units, so the 0 goes to 2

Answer 22

how about choice B?

Answer 23

(-2, infinity) since it shifts down 2 units

Answer 24

very good

Answer 25

C would be (2, infinity) and D. would be (-2,infinity). there fore the answers are A and C

Answer 26

A and C are correct

Answer 27

this is of course assuming the two functions for A and C are

\[\Large f(x) = 3^x + 2\]

and

\[\Large f(x) = 0.25^x + 2\]

Answer 28

now say you have an x value restriction would it just have an number instead of -infinity like say (1,infinity)? and yes that is what the two functions were

Answer 29

what do you mean by your first question?

Answer 30

like how you said 1/x-1 you cannot have x=1 b/c the denominator equals zero you cannot divide by zero so what would the domain be?

Answer 31

oh if you have a restriction that x cannot equal 1, but it can equal any other number, then you basically start out with (-infintity, infinity)

then you "poke a hole" at x = 1, aka you remove 1, to get this

(-infintity, 1) U (1, infinity)

Answer 32

Saying (-infintity, 1) U (1, infinity) is another way of saying

"you can pick any number you want that's either less than 1 or greater than 1. You cannot choose 1 itself"

Answer 33

ok thanks that makes a lot more since. i have a few quick questions to ask if you dont mind they are true and false i will tell you what i think it is i just want to know if i am right

Answer 34

sense*

Answer 35

sure, go ahead

Answer 36

i believe this is true