I am confused of shifting a linear equation. Let f(x)=ax+b And g(x) is identical to f(x+2)+5 For example, we create a specific condition, g(x)=f(x) and (1,2) is a point on f(x) [Does this implies that (1,2) is also a point on g(x)?] Next step is to find f(x): By using the given conditions, f(x)= -5x/2+9/2 The contradiction appears: g(x)=f(x+2)+5 That's mean shifting the whole curve of f(x) to left parallel to x-axis by 2 units, then by shifting it upwards by 5 units, we get g(x). My answer to the previous question ( typed in bold ) is yes but I am not certain with my answer. If I am correct, then the point hasn't moved away. However, it's clear to know that the shifting must move the point upward DUE TO A VECTOR NATURE. My contradiction is here, anyone helps me solve it?