How to Reflect a Function's Graph

Reflections of a graph take the parent function and provide a mirror image of it over either a horizontal or vertical line. You’ll come across two types of reflections:

• A negative number multiplies the whole function

  

  The negative outside the function reflects across a horizontal line, because it makes the output value negative if it was positive and positive if it was negative.

  Look at the above figure, which shows the parent function

  

  and the horizontal reflection

  

  If you find the value of both functions at the same number in the domain, you’ll get opposite values in the range. For example, if x = 4, f (4) = 16 and g (4) = –16.

• A negative number multiplies only the input x

  

  Vertical reflections work the same as horizontal reflections, except the reflection occurs across a vertical line and reflects from side to side rather than up and down. You now have a negative inside the function.

  For this reflection, evaluating opposite inputs in both functions will yield the same output. For example, if

  

  you can write its vertical reflection as

  

  When f (4) = 2, g (–4) = 2 as well (check out the graph in the above figure).