Question

i need help with domain

Answer 1

what is the domain of the graph?

Answer 2

The domain is the set of X values that this function can take on.

So it appears we have a quadratic function, opening downward.
The function that is graphed I think actually would look like this,
\(f(x)=-(x-2)^2+3\)

So the question is, what X values are you allowed to plug into that function? :O Hmmm..

Answer 3

x ≥ 2

x ≤ −1

Answer 4

There is no square root, no dividing by x, no fractional exponent. There is nothing that we have to worry about when plugging values in for X.

If we plug in -1 bajillion, we'll get a really big negative number for f(x), but it's still a real number.

Answer 5

?

Answer 6

Since it's simply a quadratic, there are NO restrictions on the X term.
The domain is ALL real numbers. :)

You won't run into domain restrictions when you have nice polynomials like this - just simple powers of X.

Answer 7

oh ok can you help me with this too? What is the range of the graph of y = −2x^2 − 8x − 7?

Answer 8

So this one is similar to the last one. It will be a parabola opening DOWNWARD.

Unfortunately, they didn't give it to us in vertex form. So let's convert it so it's a little easier to see what's going on.

Answer 9

(-2,1)

Answer 10

as the vertex maybe

Answer 11

Oh man yer a lot faster at that than I am XD haha

Answer 12

i use graphing tech

Answer 13

Oh hah c:
Well I wouldn't rely TOO MUCH on that, unless of course you're allowed to use it on a test ^^

Answer 14

i am they give us graphing calculators

Answer 15

Oh good good ^^

Answer 16

:)}]

Answer 17

So we have the vertex of our parabola at (-2,1) and it's opening downward (because of the negative sign on the x^2 term).

So similar to the last problem, if we put in -2 bajillion for x, we'll get a really huge negative number for Y.

But in this problem, if you graphed it, you may have noticed that we can't get any Y values larger than our vertex.

The range represents the Y values the function can take on.

So what would your range be? :O

Answer 18

y ≤ −2?

Answer 19

The -2 represents the X value of our vertex. (-2,1).

Answer 20

oh so y ≤ 1

Answer 21

So Y can get as large as 1, and as negative as it wants?
Yah that sounds right c: good job.

Answer 22

ok thanks :)