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 `frac(1)(a)` 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 `frac(1)(5)`

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

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