The black graph is the graph of y= f(x). Choose the equation for the red graph which one: a, b, c, d?

Option C.

Step-by-step explanation:

First, let's define the transformations used here:

We can see that the red graph is shifted horizontally to the right, and that is reflected across the x-axis:

Horizontal shift:

For a general function f(x) an horizontal shift of N units is written as:

g(x) = f(x + N)

where:

If N > 0, the shift is to the left

if N < 0 , the shift is to the right.

Reflection across the x-axis.

For a function f(x), a reflection across the x-axis is just written as:

g(x) = -f(x)

So, if here we have a reflection across the x-axis and a horizontal shift of one unit to the right, we would write the equation for the red graph as:

g(x) = -f(x)     (only for the reflection)

g(x) = -f(x - 1)    (for the reflection and the shift)

Then the graph of the red function is:

y = -f(x - 1)

We can rewrite this as:

y = -1*f(x - 1)

dividing both sides by -1 we get:

y/-1 = f(x - 1)

This is what we can see in option C, so the correct option is C.