Question

Please Help!?!?
Sketch the graph of
f(x)={ x^2+4x+2, x<-2
{1-4x-x^2, x>_ -2

(It is one big bracket)

also if you can

(a) Is f continuous at x=-2?
(b) Is f differentiable at x=-2? Explain

Answer 1

Please help me, i really have no idea how to do this

Answer 2

pick some numbers for x, and figure out what f(x)
for example, at x=0, f(x) = 0^2 + 4*0 + 2 = 0+0+2 = 2
so (0,2) is a point on this parabola.
try x=-1, x=-2 x= -3,

note that they only want the curve for x < -2, but it does not hurt to plot the whole thing and then "erase" the part they don't want.

Answer 3

how do i graph it though? like what should the graph look like?

Answer 4

@phi

Answer 5

This will help

http://www.khanacademy.org/math/algebra/algebra-functions/graphing_functions/v/graphing-a-quadratic-function

Answer 6

is it the same for the type of function I have to graph?

Answer 7

yes

Answer 8

the example is closer to your second equation
1-4x-x^2 (this one looks like a "frown"

Answer 9

lol its just i didn't know how to express the inequality

Answer 10

because it is a greater than sign

Answer 11

f(x)={ x^2+4x+2, x<-2
{, x≥ -2

this means that when x is less than -2, you use the top equation
when x is -2 or bigger, you use the bottom equation

For the time being, ignore the x<-2 or x≥ -2
just plot the top equation (use a table of values like in the video)
then do the same for the bottom equation
after you are done, at x<-2, erase the bottom equation's curve
at at x≥ -2 , erase the top equation's curve.

It will look something like this