Translating right uses x−5 because horizontal shifts modify the input variable inside the function argument. To shift the graph right by h units, you must replace x with x−h so that the function evaluates the original input at a point h units to the left, effectively moving the graph right.
Conditions: The transformation is a horizontal translation of the graph of y=f(x).; The shift amount is a positive constant.
Translating right uses x−5 because horizontal shifts modify the input variable inside the function argument. To shift the graph right by h units, you must replace x with x−h so that the function evaluates the original input at a point h units to the left, effectively moving the graph right.
Conditions: The transformation is a horizontal translation of the graph of y=f(x).; The shift amount is a positive constant.
Moving left uses plus inside the function argument because horizontal translations modify the input variable. To shift the graph left by h units, you must replace x with x+h so that the function evaluates the original input at a point h units to the right, effectively moving the graph left.
Conditions: The transformation is a horizontal translation of the graph of y=f(x).; The shift amount is a positive constant.
Moving left uses plus inside the function argument because horizontal translations modify the input variable. To shift the graph left by h units, you must replace x with x+h so that the function evaluates the original input at a point h units to the right, effectively moving the graph left.
Conditions: The transformation is a horizontal translation of the graph of y=f(x).; The shift amount is a positive constant.