Sagot :
Answer:
D is the answer
Step-by-step explanation:
plug the -2's in line 1 & 2 then 4 in 2 and 3
the 1&2 , and the 2 and 3 numbers have to match
Using the conditions for continuity, we find that the function D.) is continuous.
How to check if a function is continuous?
A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:
- f(a) exists (i.e. the value of f(a) is finite)
- the right-hand limit = left-hand limit, and both are finite.
- right-hand limit = left-hand limit = f(a)
Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:
A.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 6 = 4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
B.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 -2 = -4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
C.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 25 - 3*4 = 13
left hand limit = 0.5 * (4)² = 8
right hand limit = 25 - 3*4 = 13
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.
D.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 20 - 3*4 = 8
left hand limit = 0.5 * (4)² = 8
right hand limit = 20 - 3*4 = 8
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.
Thus, the function is continuous.
Learn more about continuity here
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