Question

if the domain is {-3> or equal to x < or equal to}, state the range for
f(x)^2 + 4
and
g(x) = |x+1|

Answer 1

@jim_thompson5910

Answer 2

"{-3> or equal to x < or equal to}" seems all messed up

Answer 3

also the same with "f(x)^2 + 4"

Answer 4

\[-3\le x \le 3\]

Answer 5

\[f(x)= x^{2} +4\]

Answer 6

what you can do is go to this graphing calculator here

https://www.desmos.com/calculator

and type in each function. You would then place the domain at the end in curly braces

example: x^2+4{-3 <= x <= 3} would plot f(x) based on that restriction

Answer 7

then use the graph to read off the range

Answer 8

we're not allowed to use graphing calculators

Answer 9

ok plug in the x values of the domain into f(x) to get values that lie in the range of f(x)

the range will span from the smallest output to the largest output

Answer 10

oh so (-3)^2 + 4 and then (3) ^2 + 4

Answer 11

isnt it just 13?

Answer 12

that is the largest value in the range of f(x), what is the smallest?

Answer 13

isnt that 13 too the - becomes positive 9 +4 so theyre both 13

Answer 14

you have to plug in all the x values between -3 and 3

Answer 15

ohh

Answer 16

and see which y value is the smallest and which is the largest

Answer 17

oh so 4

Answer 18

\[4\le x \le 13\]

Answer 19

yes so the range is \[\Large 4 \le y \le 13\]

Answer 20

use y instead of x for the range

Answer 21

oh right y yeah thanks!

Answer 22

you'll do the same for g(x)

Answer 23

so i got \[1\le y \le4\]

Answer 24

there's a value smaller than 1

Answer 25

how?

Answer 26

the lowest is 0+1

Answer 27

did you try any negative x values to plug in?

Answer 28

yeah but its absolute value so everythings positive

Answer 29

what x values did you try so far

Answer 30

oh i see what i did so the lowest is 0 right?

Answer 31

yes so the range for g(x) is \[\Large 0 \le y \le 4\]

Answer 32

yeah got it! thanks so much!

Answer 33

yw