Answer:
(a) 1
(b) 1 3/4
(c) [-2, 4]
(d) [-1/4, 2]
Explanation:
Apparently, the vertex of the graph is (1, 2) and it goes through points (-1, 1) and (3, 1). In vertex form, the equation for this is ...
y = a(x -1)^2 +2
We can find the value of 'a' from the point (3, 1):
1 = a(3 -1)^2 +2 = 4a +2 . . . . substitute for x and y, and simplify
-1 = 4a . . . . . . . subtract 2
-1/4 = a . . . . . . divide by 4
So, ...
f(x) = -1/4(x -1)^2 +2
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(a)
Above, we assumed point (-1, 1) was on the graph:
f(-1) = 1
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(b)
Using the equation we found, ...
f(2) = -1/4(2 -1)^2 +2 = -1/4 +2
f(2) = 1 3/4
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(c)
The domain is the horizontal extent of the graph, apparently from x = -2 to x = 4.
domain: [-2, 4] or -2 ≤ x ≤ 4
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(d)
The range is the vertical extent of the graph. The minimum can be found at the end of the domain:
f(4) = -1/4(4 -1)^2 +2 = -9/4 +2 = -1/4
The maximum has already been established as the vertex at y=2.
range: [-1/4, 2] or -1/4 ≤ y ≤ 2