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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.

Respuesta :

C.


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


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


So, if you draw the two graphs, you will associate two opposite [tex] y [/tex] values to the same [tex] x [/tex] value.


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

lublana

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

[tex](x,y)\rightarrow (x,-y)[/tex]

Suppose, f(x)=x+1

[tex]-f(x)=-(x+1)[/tex]

Hence, the graph flips over the x- axis.

Ver imagen lublana

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