Given the g(x)=f(x) + k, identify a value of k that transforms f into g

a vertical shift of 6 units up

Step-by-step explanation:

We have the transformation:

g(x) = f(x) + k

This is what we call a vertical shift, this transformation moves the graph of f(x) k units, and the motion is upwards if k is positive, and downwards if k is negative.

Here we can see that the graph of f(x) intersects the y-axis at y = -2

While the graph of g(x) intersects the y-axis at y = 4.

Then the distance between these two points is:

4 - (-2) = 6

This means that the graph of g(x) is 6 units above the graph of f(x)

Then we have that k must be equal to 6, then the transformation is:

g(x) = f(x) + 6

This is a vertical shift of 6 units up.

the answer to the expression is 83