Question

can someone help me understand how to find the domain and range of y=-2|x-1|+4

Answer 1

Theres no restriction on domain, you can take the absolute value of both positive and negative numbers so domain would be all real numbers

Answer 2

Domain: all real numbers will do, because you can take the absolute value of any number.

Range: first look at the range of |x|: all the nonnegative numbers.

Now you have done some calculations with this: instead of |x| there is |x-1|.
This has no impact on the range, because x-1 too is sometimes positive, sometimes negative, but the absolute value just makes it nonnegative.
Then there is the factor -2.
What happens if you multiply a nonnegative number with -2?
It makes all these numbers negative! (or zero if it was zero to begin with...).
So the range of -2|x-1| is: all the numbers <= 0.
Finally add 4 to these numbers. Now ask yourself which numbers you get...
Now you have the range!

Hope this helps.

ZeHanz

Answer 3

Add 4 to what numbers.

Answer 4

See your formula: y = -2|x-1| + 4 <=== there is the 4

Answer 5

yes but what do i do with it

Answer 6

its helpful to know about shifts and reflections as well as knowing what the basis graph looks like

Answer 7

y = |x| is the basic graph, which shows that the
basic domain is all reals. and range is 0 to inf

a shift by any real value "c" has no effect on this graph

multiplying |x| by a negative value flips it about the x axis

Answer 8

all that does is negate the range from 0 to inf, into 0 to -inf

adding on a real value "d" moves the graph vertically (and hence the range) by "d"

Answer 9

so what the range would be 4

Answer 10

all the range values would be increased by 4 in this case, yes

(0,-inf) + 4 = (4,-inf)

Answer 11

so yes it is 4

Answer 12

if it is then i get it if not im lost

Answer 13

the range is not "4"; it just starts at 4

Answer 14

so its 4-infinity

Answer 15

4 to (negative infinity)

Answer 16

why negative

Answer 17

re read up a few posts at:

y = |x| is the basic graph, which shows that the
basic domain is all reals. and range is 0 to inf

a shift by any real value "c" has no effect on this graph

multiplying |x| by a negative value flips it about the x axis

Answer 18

So its negative because of the negative 2 at the beginning

Answer 19

correct

Answer 20

Awesome I get it now! Thanks.

Answer 21

good luck :)

Answer 22

wait your smart at this so how would i use the vertex and the sign a to determine the range?