Sketch Reflections of Functions

Sketch Reflections of Functions

GCSE(H)

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:

`y=f(-x)` will reflect the function `y=f(x)` 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:

`y=-f(x)` will reflect the function `y=f(x)` in the `x`-axis.

Examples

1. Sketch the graph of the function `f(x)=3x+4`. On the same graph, sketch `f(-x)`. Label the graph.

Answer: sketch of y=3x+4 and y=3(-x)+4

2. A function is given by `f(x)=3sin(x)`. The function returns a value of -3 when `x=270ยบ`. Sketch the graph for `f(-x)` where 0 < x < 360.

Answer: sketch of y=3sin(-x)