How do I choose between these two answers?

[StringFever]

Hi guys,

Just a quick question about NEAP 2008 Exam 2 (MC Q1)

The function g: [a,b] --> R, g(x) = 2 - (2x+1)^2 has a range [-7,2].
The values of a and b could be:

A) WRONG
B) a= -0.5, b= 2
C) a = -0.5, b=1
D) WRONG
E) WRONG

I'm stuck between B and C, and was wondering how I could get the right answer (which, BTW, is C).

Thanks for the help and + 1 for any one who helps!

[THem]

when x = 2 g(2) = 2-(5)^2 = 2-25 = -23
When x = 1, g(1) = 2-(3)^2 = 2-9 = -7

[Over9000]

Sketch the graph, its inverted (unhappy face)
So we get the max of the range 2, from the T.P.

To find at what points y=-7, let y=-7 in the equation
(You can do this because we know the graph extends until negative infinity unless restrictions are applied so the point at which the graph is most negative would be where the restriction is applied however, sketching it on ur calc would be easier, imput and then looking where the graph is at y=2 and where it is at y=-7 (the x values of these points)







Since the options have you choose between 1 and 2, it would be b=1.

[StringFever]

when x = 2 g(2) = 2-(5)^2 = 2-25 = -23
When x = 1, g(1) = 2-(3)^2 = 2-9 = -7

God I'm an idiot, I didn't see the 2 in front of the x!!!!

[mtwtfss]

Just chuck into ya calc: y1: 2-(2x+1) y2: -7 y3: 2

and find the intersections from these lines, and you'll be fine