By adding some number to every function value,
its graph is vertically. To instead translate it horizontally, a number is subtracted from the input of the function rule.
The number h
is subtracted and not added, so that a positive h
translates the graph to the right.
Translate graph to the right
Translate graph upward
Notice that if the quadratic function f(x)=ax2
is translated both vertically and horizontally, the resulting function is
This is exactly the of a quadratic function. The of f(x)=ax2
is located at (0,0).
When the graph is then translated h
units horizontally and k
units vertically, the vertex moves to (h,k).
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
A graph is instead reflected in the y
-axis, moving all points on the graph to the opposite side of the y
-axis, by changing the sign of the input of the function.
Note that the is preserved.
A function 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