Graphs can be stretched horizontally and vertically by applying scale factors. If the factor is applied before the function is evaluated, then the stretching takes place parallel to the x-axis, but the amount of stretching is a reciprocal of the factor:
Mapping f(x) onto f(ax) stretches a graph by factor 1a on the x-axis.
If the factor is applied after the function is evaluated, then the stretching takes place parallel to the y-axis:
Mapping f(x) onto af(x) stretches a graph by factor a on the y-axis.
Sketch the graph of the function f(x)=sin(x). On the same graph, sketch f(5x).
Describe the transformation.
A multiple applied before the function is evaluated will expand by a scale factor of the reciprocal of the multiple along the x-axis.
Answer: The curve is enlarged parallel to the x-axis with a scale factor of 15
Sketch the graph of the function f(x)=sin(x). On the same graph, sketch 5f(x).
Describe the transformation.
A multiple applied after the function is evaluated will expand by a scale factor of the multiple in the direction of the y-axis.
Answer: The curve is enlarged parallel to the y-axis with a scale factor of 5
See also Expressions as Functions and Enlargement