Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.

Solution:

Given: Equation is g(x) = f(x) + k --- (A)

From the graph, we can say that there is a shift of 3 units up between f(x) and g(x)

As they are parallel lines, their slopes will be the same but intercepts will be different.

The y-intercept of f(x) = 2 and that of g(x) = 5

Here, the difference between the intercepts is 3

So we can write it as g(x) = f(x) + 3 --- (B)

By comparing (A) and (B)

We can say that k = 3

Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.

Summary:

Given f(x) and g(x) = f(x) + k, from the graph, we can determine the value of k as 3 units.