PLZ HELP IM MARKING BRAINLIEST
1 answer:
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Step-by-step explanation:
As we can see the question given
f(x) is varying accordingly to the interval
<em> f(x) = 2 if 2<x≤4</em>
The value of function is 2 for the interval 2 to 4
and interval is open at x=2 and closed at x = 4
<em> f(x) = x + 3 if 4<x<8</em>
The value of function is x + 3 and it is open at x = 4 and x = 8
<em>f(x) = 2x if x 8</em>
The value of function is 2x for x greater than or equal to 8
The image is attached for more clearing of doubt
Answer:
A. Domain : (-∞, ∞)
B. Function is increasing in the interval (-2, 0) and (2, ∞)
Decreasing in the interval of (-∞, -2) and (0, 2).
Step-by-step explanation:
A. Given function is, y = |2x - 1|
This function is the transformed form of the parent function, y = |x|
Domain of the parent function is { x | x is a set of real numbers}
Therefore, domain of the transformed function will be the same as the domain of the parent function.
Domain of the function = {x | x is a real number}
B. Given function is f(x) =
Domain of the function : (-∞, ∞)
Critical points of the function are,
⇒ x = 0, ±2
Now we find the three intervals where we have to check the function to be increasing or decreasing.
(-∞ -2), (-2, 0), (0, 2), (2, ∞)
Derivative of the function f(x),
f'(x) =
Here, f'(x) < 0 for (-∞, -2)
f'(x) > 0 for (-2, 0)
f'(x) < 0 for (0, 2)
f'(x) > 0 for (2, ∞)
Therefore, given function is increasing in the interval (-2, 0) and (2, ∞)
And it's decreasing in the interval of (-∞, -2), and (0, 2).
