The function that has its only zero at x=–4 is f(x) = |x+4|. The correct option is A.
What is Absolute Value?
An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number. for example, |-5| will give 5, and also, |5| will give 5 as well.
The function that has its only zero at x = –4 can be found by substituting the value of the function equal to 0.
A.) f(x) = |x+4|
when x > 0
f(x) = 0
x + 4 =0
x = -4
when x < 0
f(x) = 0
-x - 4 =0
-x = 4
x = -4
B.)
f(x) = |x| + 4
when x > 0
f(x) = 0
x + 4 =0
x = -4
when x < 0
f(x) = 0
-x + 4 =0
-x = -4
x = 4
C.) f(x) = |x - 4|
when x > 0
f(x) = 0
x - 4 =0
x = 4
when x < 0
f(x) = 0
-x + 4 =0
-x = -4
x = 4
D.) f(x) = |x| - 4
when x > 0
f(x) = 0
x - 4 =0
x = 4
when x < 0
f(x) = 0
-x - 4 =0
-x = 4
x = -4
Hence, the function that has its only zero at x=–4 is f(x) = |x+4|.
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