g(x) is basically transformed f(x). First, let's focus on f(x) graph. Notice how the graph has slope of 1 and intersect y-axis at (0,0).
Which means that our equation for f(x) is:
[tex] \large{f(x) = x}[/tex]
Now then we focus on g(x). g(x) is f(x+k). That means if f(x) = x then f(x+k) would mean substitute x = x+k in the equation.
[tex] \large{f(x + k) = x + k }\\ \large{g(x) = x + k}[/tex]
Next, we want to find the value of k. In the slope-intercept form or y = mx+b where m = slope and b = y-intercept. Notice the g(x) graph and see that the graph intersects y-axis at (0,4). Therefore k = y-intercept = 4.
[tex] \large{g(x) = x + 4}[/tex]
Answer
- g(x) = x+4
- Therefore the value of k is 4.
