Hybrid Functions - so confused :(

[hello_kitty]

Hey Guys,
Im a bit confused on hybrid functions,
is there a process i should use to be able to do hybrid functions?

for example

f(x) = -x , x < 1    &      x, x ≥ 1

What i did first, was solve for the x and y intercepts..which for both equations are (0,0)

Then it shows points such as (1,-1) for the first graph,  and (1,1) for the second graph..
Is that just substituting another point?

I'm just confused on how to approach hybrid function questions. any helpw ould be great!

Thanks x

[pi]

Then it shows points such as (1,-1) for the first graph,  and (1,1) for the second graph..
Is that just substituting another point?

These are the 'end-points' of each part of the hybrid function. These are found by substituting the restricted domain into its respective hybrid part. eg. subbing 1 for x into y=-x (open circle), and 1 for x into y=x (closed circle).

[xZero]

If you're wondering how to graph hybrid functions, just think of it as 2 separate functions.

Draw f(x) = -x, x < 1 then draw f(x) = x, x ≥ 1. Put the inclusive/exclusive circles at the end points and your done.

[hello_kitty]

So the points i kno to sub in are the resticted domains?

for example:

f(x) =      x -2 , x < -2 (i would sub in -2)??
      =      x^2 - 4, -2 ≤ x ≤ 2  (what would i sub in here? -2 or 2? Because I thought you just put the -4 as the y intercept when x = 0??

      = x + 2, x > 2  (would i sub in 2?)


Also, how do i graph and work it out if there is a negative in the hybrid functions?

f(x) =  1/x   , x < 0   (sub 0?)

      =  x + 1 , x ≥  0 (sub 0 ?)


with both of these examples, how do i find the range, because for the first example i posted on the thread, it said it is (-1, infinity) im just not sure how that is the range.

Thanks!

[/0]

If you're looking for a y-intercept, then you require that . Note that you can only possibly have in the left branch of the graph, since the right branch has . So plugging into left of the graph, you get the y-intercept (0,0).

Also, the point (1,-1) isn't part of the graph, since that would belong to the left branch, but the left branch has . It is an open circle. The point (1,1) is part of the graph, specifically the right branch.

[hello_kitty]

so would you say when sketching hybrid functions  you would:

determine if their liner or quadratic
then look at the domains of each equation and sub them into the equation
then draw the grapph
and then choose to part in relation to the domain?

[luffy]

so would you say when sketching hybrid functions  you would:

determine if their liner or quadratic
then look at the domains of each equation and sub them into the equation
then draw the grapph
and then choose to part in relation to the domain?

Have you ever sketched graphs under restricted domains? For example, sketch under a domain of ?
If so, then a hybrid function is just sketching a few graphs of restricted domains on a single axes.

To answer your question:
1. It will not always be linear or quadratic. It may be exponential, logarithmic, sinusoidal etc as well.
2. Yes, definitely look at the domains and sketch each component of the hybrid under the restricted domain.

Hope I helped.

[TrueTears]

so would you say when sketching hybrid functions  you would:

determine if their liner or quadratic
then look at the domains of each equation and sub them into the equation
then draw the grapph
and then choose to part in relation to the domain?

correct but ignore the first step, hybrids don't always be have to be linear or quadratic.

also i dont know what u mean by "sub them into the equation", i guess just be aware of the domain and sketch the graph according to the domain.

[hello_kitty]

kay thanks! ive done some questions and i think im starting to get the hang of it!
thanks guys

however, theres one thing i dont understand, how do i specify the function of a represented graph?

for example i attached on another threat, because i'm not sure how to attach a photo in a reply!

[hello_kitty]

i added it to the top of this thread