The zeros of a function are the values of x, when the function equals 0.
The function that has zeros of -8, 1 and 3 is: (a) [tex]\mathbf{ y = (x - 3)(x + 8)(x - 1)}[/tex]
The zeros are given as:
[tex]\mathbf{Zeros = -8, 1, 3}[/tex]
Rewrite as:
[tex]\mathbf{x = -8, 1, 3}[/tex]
Equate to 0
[tex]\mathbf{x +8 = 0,\ x - 1 = 0,\ x - 3 = 0}[/tex]
Multiply the equations
[tex]\mathbf{(x +8) \times (x - 1) \times (x - 3) = 0\times 0 \times 0}[/tex]
[tex]\mathbf{(x +8) \times (x - 1) \times (x - 3) = 0}[/tex]
Express as a function
[tex]\mathbf{y = n(x +8) \times (x - 1) \times (x - 3) }[/tex]
Where:
[tex]\mathbf{n \ne 0}[/tex]
The above equation represents functions that have zeros of -8, 1, and 3
By comparing the options, we have:
[tex]\mathbf{ y = (x - 3)(x + 8)(x - 1)}[/tex] is [tex]\mathbf{y = n(x +8) \times (x - 1) \times (x - 3) }[/tex], where n = 1
Hence, the function that has zeros of -8, 1 and 3 is:
(a) [tex]\mathbf{ y = (x - 3)(x + 8)(x - 1)}[/tex]
Read more about zeros of functions at:
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