G(x)= 3 - |2x-4| is defined for the domain -1 < x < 6.
1 answer:
(a) The range of g is the set of y values that g covers for the given domain. Given the shape of g, you will be interested in the starting point and ending point g(-1)=1, g(6)=-5 and the tip of g, which is where |2x-4|=0, ie., x=2. g(2) =3.
The highest encountered g is 3 (at x=2). The lowest one is -5 (at x=6). Note that the highest is inclusive, the lowest is exclusive (since x=6 is not part of the domain).
So the range is (-5,3].
(b) Solve g(x) = 2, then find the x values that cause g(x)>2.
g(x)=2 => 3-|2x-4| = 2 => |2x - 4| = 1 => | x-2 | = 1/2
x-2 = 1/2 or 2-x = 1/2 => x=5/2 or x=3/2
From the graph you can see that x has to be in between these values, so the solution is:
3/2 < x < 5/2.
The values themselves are excluded (ie., no ≤) since g(x) > 2 and not ≥ 2
The highest encountered g is 3 (at x=2). The lowest one is -5 (at x=6). Note that the highest is inclusive, the lowest is exclusive (since x=6 is not part of the domain).
So the range is (-5,3].
(b) Solve g(x) = 2, then find the x values that cause g(x)>2.
g(x)=2 => 3-|2x-4| = 2 => |2x - 4| = 1 => | x-2 | = 1/2
x-2 = 1/2 or 2-x = 1/2 => x=5/2 or x=3/2
From the graph you can see that x has to be in between these values, so the solution is:
3/2 < x < 5/2.
The values themselves are excluded (ie., no ≤) since g(x) > 2 and not ≥ 2
You might be interested in
296 cm is your answer Cody.
A easier way to do this question with coming on to brainly. Is add all the positive Integers OR Numbers together and then add all the negative numbers together. Then subtract the negative numbers from the positive. Something like this.
