Question

Pre-calculus 12 Question!



The zeros of a function y= f(x) are -3 , 0 , 2. Determine the zeros of the function y= f (1 - x).

a) -4, -1, 1
b) -3, -1 , 2
c) -2, 1 ,3
d) -1, 1 ,4

Answer 1

f(1-x) = f(-x+1)
f(1-x) = f(-(x-1))

so the graph of f(x) is mirrored over the y axis and we shift 1 unit to the right to get the graph of f(1-x)

Answer 2

@jim_thompson5910 so, the answer is a. Am I right?

Answer 3

-(-3-1)= -4 for the domain?

Answer 4

put another way, if x = -3, then f(-3) = 0 since we're told that -3 is a root

so

f(1-x) = f(1-(-3)) = f(1+3) = f(4)

making 4 a root of f(1-x)

Answer 5

Oh I see now.

So any number inside the bracket of f( ) is a root of that function?

Answer 6

`The zeros of a function y= f(x) are -3 , 0 , 2`

-3 is a root of f(x)
0 is a root of f(x)
2 is a root of f(x)

Answer 7

`-3 is a root of f(x)` ----> `f(-3) = 0`
`0 is a root of f(x)` ----> `f(0) = 0`
`2 is a root of f(x)` ----> `f(2) = 0`

Answer 8

Right, thank you for clarifying it for me. :)

Answer 9

sure thing