The can be applied to as usual.
By adding some number to every function value,
a function graph is vertically. Notice that the horizontal changes, while the vertical one is unaffected.
A graph is translated horizontally by subtracting a number from the input of the function rule.
Note that the number, h,
is subtracted and not added. This is so that a positive h
leads to a translation to the right, which is the positive x
-direction. This transformation affects the vertical asymptote, but not the horizontal.
Translate graph to the right
A function is in the x
-axis by changing the sign of all function values:
Graphically, all points on the graph move to the opposite side of the x
-axis, while maintaining their distance to the x
-axis. Thus, x
-intercepts and vertical asymptotes are preserved.
A graph is instead reflected in the y
-axis by moving all points on the graph to the opposite side of the y
-axis. This occurs by changing the sign of the input of the function.
Notice that the and horizontal asymptote are preserved.
A function's graph is by multiplying the function rule by some constant a>0
All vertical distances from the graph to the x
-axis are changed by the factor a.
Thus, preserving any .
By instead multiplying the input of a function rule by some constant a>0,
its graph will be by the factor
Since the x
-value of is 0,
they are not affected by this transformation.
Stretch graph horizontally