In this lesson, we will learn how to reflect a graph on the x- or y-axis, both graphically and algebraically.

Students will be able to

Students should already be familiar with

Students will not cover

Q1:

Graphs 𝐴 and 𝐵 in the diagram are the graphs of square root functions. They are symmetric about the origin. The equation of graph 𝐴 is 𝑦=13√𝑥+2+1. Knowing that a point reflection about the origin is equivalent to a reflection in the 𝑥-axis followed by a reflection in the 𝑦-axis, find the equation of graph 𝐵.

Q2:

Which of the following processes would you use to obtain the graph of 𝑦=−𝑓(−𝑥) from the graph of 𝑦=𝑓(𝑥)?

Q3:

Consider the square root function 𝑓(𝑥)=𝑎√𝑥−ℎ+𝑘.

This function is a transformation of 𝑦(𝑥)=√𝑥. Where is the origin mapped to in the graph of 𝑓?

The graph of the function 𝑝 is obtained by reflecting the graph of 𝑓 in the 𝑥-axis. What is the equation of 𝑝?

The function 𝑦 can be transformed to 𝑝. Where is the origin mapped to in the graph of 𝑝?

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