Primarygun Posted May 11, 2005 Share Posted May 11, 2005 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? Link to comment Share on other sites More sharing options...
uncool Posted May 11, 2005 Share Posted May 11, 2005 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- Link to comment Share on other sites More sharing options...
Primarygun Posted May 12, 2005 Author Share Posted May 12, 2005 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 ? Link to comment Share on other sites More sharing options...
Primarygun Posted May 12, 2005 Author Share Posted May 12, 2005 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. Link to comment Share on other sites More sharing options...
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