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?

g(x) = f(x+2) + 5 = -5(x+2)/2 + 9/2 = -5x/2 -5 + 9/2 + 5 = -5x/2 + 9/2

It is because you are moving the line in the same direction as the line is going - the slope is -5/2, or 5 units up over -2 units to the left - which is what you said.

However, (1,2) goes to (3,7).

-Uncool-

Thanks for reply first. How is the point (3,7) archieved?

g(1)=f(1+2)+5

Isn't the variable,i.e., the x-coord. is 1 ?

Once the function f(x) is changed to g(x)=f(x+2)+5,

that means it shifts left by 2 and upwards by 5.

Obviously, the new point is not the original point as it has moved upward along the original line.

This is a general case for all linear equations.

However, as I mentioned, if I let f(x)=g(x), moreover, (1,2) lies on the equation,...........then f(1)=2 ---> g(1)=2

That means the point didn't move.

How to explain the italic sentence?

My solution: The line is shifted 2 units leftwards and then 2 units rightwards for that specific equation.