Question

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

Answer 1

Answer:

C.The graph flips over the x- axis

Step-by-step 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.