Question

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

Answer 1

It ceases to be increasing and becomes decreasing in the case of a 1st degree equation.

Answer 2

The graph is reflected about x-axis.

Explanation:

Since, rule of reflection across x-axis,

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

And, the rule of reflection across y-axis,

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

Thus, when a function f(x) is reflected across x-axis,

Then, the transformed function is -f(x),

While, when f(x) is reflected across y-axis,

The transformed function is -f(x),

Hence, we can say that,

When a function is multiplied by -1, it will reflect about x-axis.