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Sketch Reflections of Functions

Sketch Reflections of Functions

Graphs can be reflected by applying negative values to a function.

If the negative value is applied before the function takes place, then the result is a reflection in the y-axis.

If the negative value is applied to the result of the function, then the reflection will take place in the x-axis:

Example 1

Sketch the graph of the function `f(x)=x^2`. On the same graph, sketch `-f(x)`.

Describe the transformation.

A negative value applied after the function is evaluated will reflect the curve in the `x`-axis.

Answer: The curve is reflected in the `x`-axis.

Graph showing reflection function then amend answer

Example 2

Sketch the graph of the function `f(x)=x^2`. On the same graph, sketch `f(-x)`.

Describe the transformation.

A negative value applied before the function is evaluated will reflect the curve in the `y`-axis.

Answer: The curve is reflected in the `y`-axis.

Graph showing reflection amend value then function

See also Expressions as Functions and Reflection