Question

how do you graph an equation y=a*f(x+h)-k something like this

Answer 1

Start with the graph of f(x)


then stretch the graph by a factor of 'a' (this will depend on if |a| > 1 or |a| < 1)


if a < 0, then flip the graph over the x axis


now shift the graph to the left/right 'h' units (this of course depends on whether h is positive or negative)


finally, shift the graph up/down k units (again this depends on whether k is positive or negative)


This is a very vague description of what's going on here, so it would be best to provide the actual function if you can.

Answer 2

i have a graph of y=f(x) which have a coordinate of (-4,-3) (-2,2) (-1,2) (1,0) (3,4) (5,4) then it ask the domain and range, after that you have to sketch the graph with this given equation y=-3*f(x+3)-3

Answer 3

is there a curve going through these points, or is the entire graph just these set of points?

Answer 4

its the set of points going up,

Answer 5

but are they connected?

Answer 6

yes

Answer 7

ok

Answer 8

the domain is the set of all allowable inputs

so if there are no holes/asympotes, then the domain is the set of all real numbers

Answer 9

is the domain the x's and the range is the y's?

Answer 10

the range is the set of all possible outputs


if there are no holes or horizontal asymptotes and each y value is hit, then the range is also the set of all real numbers

Answer 11

yes that's one way to think of it

Answer 12

ok
so i don;t really need the "a" if i know the formulas like a>1

Answer 13

i mean i dont need to graph it

Answer 14

not sure what you mean

Answer 15

i mean in my equation i have y=-3*f(x+3)-3 then i know that its a reflection because a<0, then i will move the points to the right 3 units then down 3 units

Answer 16

oh i see, yes you can follow that procedure


keep in mind that you're also scaling by 3

Answer 17

since |a| = |-3| = 3

Answer 18

are you talking about "a"?
and if you are uhm how do i scale that

Answer 19

for instance, if you have the point (1,2) and you scale it by 3, you're multiplying the y coordinate by 3 to get (1, 6)

Answer 20

ohh, so im multiplying the reflection coordinates by 3 then

Answer 21

yes

Answer 22

ok now i get it :D
thanks a lot, I appreciate it

Answer 23

np