Given g(x)=f(x)+k, what value of k transforms function f into g? The value of k that transforms function f into g is what?

To help you visualize the concept of a vertical shift, consider thaty=f(x).y=f(x).Therefore,f(x)+kf(x)+kis equivalent toy+k.y+k.Every unit ofyyis replaced byy+k,y+k,so the y-value increases or decreases depending on the value ofk.k.The result is a shift upward or downward.

VERTICAL SHIFT

Given a function f(x),f(x), a new function g(x)=f(x)+k,g(x)=f(x)+k, where kk is a constant, is a vertical shift of the function f(x).f(x). All the output values change by kk units. If kk is positive, the graph will shift up. If kkis negative, the graph will shift down.