Graph the following piece wise function. State the values for f(0) and f(-2). Please show all of your work and submit graph. f(x)={x^2-3 if x-2@ 3 if-5 ≤x

Question

Graph the following piece wise function. State the values for f(0) and f(-2). Please show all of your work and submit graph.

f(x)={x^2-3     if  x>-2@ 3   if-5 ≤x< -2@-x+3   if x< -5)

anonymous · Answer

Piece wise functions are very simple. You just evaluate f(x) for a certain function depending on what range x falls into.
$$\Large f(x) = \left\{ {\begin{array}{*{20}{c}}
{x >  - 2}&{}&{{x^2} - 3}\
{ - 5 \le x \le  - 2}&{}&3\
{x <  - 5}&{}&{ - x + 3}
\end{array}} \right.$$

Just start an arbitrary x value to one side of the piecewise function, and increment (or in this case decrement) x by 1 re-evaluating at each point.
So when...
x = -1, f(x) = x^2 -3 = (-1)^2 - 3 = -2, so plot a point at (-1,-2).
x = -2, f(x) = 3, plot (-2,3)
x = -3, f(x) = 3, plot (-3,3)
x = -4, f(x) = 3, plot (-4,3)
x = -5, f(x) = 3, plot (-5,3)
x = -6, f(x) = -x+3 = -(-6) + 3 = 0, plot (-6,9)

And so on.

anonymous · Answer

is this the answer that I should use?

anonymous · Answer

can you show the graph?!

anonymous · Answer

No, because it's REAL hassle to try and get a graph on here. Can't you just plot the graph yourself?

anonymous · Answer

yes but what is the input so I can plot it?

anonymous · Answer

I havent quite figured out how to input it into wolphram alpha

anonymous · Answer

Well... the function is piece wise, so it depends on what range the input falls into. There's three functions to plot: f(x) = x^2 - 3, f(x) = 3 and f(x) = -x + 3 but at which point you plot them depends on what the value of x is at that point.

I really can't explain it any better than that.

anonymous · Answer

ok

anonymous · Answer

im just wondering how to type that into the calculator