SOLUTION: If (-1,-4) is a point on the graph of y=f(x), which of the following must be on the graph of y=-f(x)? (-1,4) (1,-4) (-4,1) (4,-1)

Algebra ->  Functions -> SOLUTION: If (-1,-4) is a point on the graph of y=f(x), which of the following must be on the graph of y=-f(x)? (-1,4) (1,-4) (-4,1) (4,-1)      Log On


   

Question 1204984: If (-1,-4) is a point on the graph of y=f(x), which of the following must be on the graph of y=-f(x)? (-1,4) (1,-4) (-4,1) (4,-1)
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
All of them but NOT (-1,4).

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: (-1, 4)

Reason

y=-f(x) tells us "reflect f(x) over the horizontal x axis"
This is because we're flipping the y or f(x) outputs from positive to negative, or vice versa.

A point like (-1,-4) flips to (-1, 4)
The x coordinate stays the same.
The y coordinate flips from -4 to 4.


An example:

f%28x%29+=+4x in green
g%28x%29+=+-f%28x%29+=+-4x in blue


Another example:

f%28x%29+=+-4%5E%28-x%29 in green
g%28x%29+=+-f%28x%29+=+-%28+-4%5E%28-x%29+%29+=+4%5E%28-x%29 in blue

Use graphing tools Desmos or GeoGebra to try out other examples.