Question

Find the domain and range of Y=x^2-9 and graph the function.

Answer 1

well, what values do you think you can give "x"?

Answer 2

It's a quadratic, and quadratics have:

domain = all reals
range = [min, infinity) if upward opening, or
range = (-infinity, max] if downward opening

Answer 3

Domain: All Real Numbers
Range: [-9, Inf)

Answer 4

Sorry guys I was in a car ride. to jdoe0001. I know the domain must be all real numbers because there are no restrictions on the x value. I do not know how to find the range though

Answer 5

well, if you notice any negative values thrown in to x^2 will go like this
\(\bf x^2\\
(-1)^2 \implies -1 \times -1 =1\\
(-10)^2 \implies -10 \times -10 =100\\
(-100)^2 \implies -100 \times -100 =10000\)

so you see, no matter what negative values you'd give to x^2, it will always throw back out a positive number
what's the lowest "x" can get? well, x= 0 => (0)^2 = 0

at that point \(\bf y=x^2-9 \implies y=(0)^2-9 \implies y = 0-9\implies y = -9\)

so, that's the lowest "y" will get, so it's range as will be no lower than -9 and up to infinity, or as boricua86 said, \(\bf [- 9, \infty)\)

Answer 6

OHH that was a great way to explain it thank you! I should be able to figure the rest of these types of problems out now. The graph is just a parabola shifted downward 9 right?

Answer 7

thanks!

Answer 8

yw