Here we need to explain what the two transformations applied to f(x) do, and then we also can see it graphically.
we can see that we have a vertical stretch of scale factor k = 0.5 followed by a vertical shift of 3 units upwards.
Now let's explain how we know that.
The two transformations applied are:
Vertical stretch:
For a given function f(x) we write a vertical stretch of scale factor as:
g(x) = k*f(x).
Which stretches or contracts the graph vertically, depending on the value of k.
Vertical shift.
For a function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N
- If N is positive the shift is upwards.
- If N is negative the shift is downwards.
So here we have:
g(x) = 0.5*f(x) + 3
Comparing with the general transformations, we can see that we have a vertical stretch of scale factor k = 0.5 followed by a vertical shift of 3 units upwards.
The two functions are:
f(x) = |x|
g(x) = 0.5*|x| + 3
The graphs can be seen below, where the blue one is the graph of g(x), the transformed function.
If you want to learn more, you can read:
https://brainly.com/question/24401156
