Question

Which equation represents a transformation of the parent function f(x) shown on the graph

Answer 1

The transformed function is:

g(x) = -f(x) - 5

Which equation shows the transformed function?

We can see that the function f(x) has an y-intercept at 0, and a slope of 1, so this is just the parent linear function:

f(x) = x

In the other hand, we can see that g(x) has a slope of -1, and an y-intercept of -5, so we have:

A reflection over the x-axis, followed by a translation of 5 units down, this is written as:

g(x) = -x - 5 = -f(x) - 5

Answer 2

From the picture showing the graph,

the function

`f(x)\text{ was firstly reflected horizontally. }`

This is represented as

`-f(x)`

Then it was further translated by 5 units. That is vertical shift downwards. Giving us

`-f(x)-5`

Hence the answer is

`g(x)=-f(x)-5`