Question

When you multiply a function by -1, what is the effect on its graph?

A. The graph flips over the line y = x.
B. The graph flips over the y-axis.
C. The graph flips over the x-axis.

Answer 1

C.The graph flips over the x- axis

Explanation:

We are given that a function multiply by -1.

We have to find the effect on its graph.

Let f(x) be the original function.

Multiply by -1 then we get

-f(x)

It means f(x) convert into -f(x).

The transformation rule when reflection across x- axis is given by

`(x,y)\rightarrow (x,-y)`

Suppose, f(x)=x+1

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

Hence, the graph flips over the x- axis.

Answer 2

C.

If you multiply a function by
`-1`, you are inverting its sign. It means that you have the parent function
`f(x)`, and the child function
`-f(x)`.

This means that, if you choose the same input
`x`, it will be mapped once to
`f(x)`, and once to
`-f(x)`.

So, if you draw the two graphs, you will associate two opposite
`y` values to the same
`x` value.

This kind of transformation,
`(x,y) \to (x,-y)` is exactly a reflection with respect to the
`x` axis.