Try reviewing this fundamentals firstTransformations the functions: Horizontal translationsTransformations that functions: upright translations

Still don't get it?Review these basic concepts…Transformations of functions: Horizontal translationsTransformations that functions: vertical translationsNope, I gained it.

You are watching: How to reflect over the y axis

Before we acquire into reflections across the y axis, make certain you've refreshed your memory on exactly how to do basic vertical translation and also horizontal translation.

Reflection across the Y-Axis

One of the most simple transformations you can make with straightforward functions is come reflect it throughout the y-axis or one more vertical axis. In a potential test question, this can be phrased in plenty of different ways, so make sure you acknowledge the following terms as simply another method of speak "perform a reflection across the y-axis":

•Graph y=f(−x)y = f(-x)y=f(−x)

•Graph f(−x)f(-x)f(−x)

•f(−x)f(-x)f(−x) reflection

•Or simply: f(−x)f(-x)f(−x)

In bespeak to do this, the process is extremely simple: For any kind of function, no issue how facility it is, simply pick the end easy-to-determine coordinates, division the x-coordinate by (-1), and then re-plot those coordinates. That's it!

The best means to practice illustration reflections over y axis is come do an instance problem:


Given the graph that y=f(x)y=f(x)y=f(x) together shown, map out y=f(−x)y = f(-x)y=f(−x).

Remember, the just step we have to do before plotting the f(-x) have fun is just divide the x-coordinates that easy-to-determine point out on our graph above by (-1). Once we say "easy-to-determine points" what this refers to is just points for which you know the x and also y worths exactly. Don't choose points wherein you need to estimate values, as this renders the trouble unnecessarily hard. Listed below are several photos to assist you visualize exactly how to fix this problem.

Step 1: recognize that we're reflecting across the y-axis

Step 2: determine easy-to-determine points

Step 3: divide these points by (-1) and also plot the new points

For a visual device to aid you through your practice, and also to check your answers, check out this wonderful link here.

How to find the Axis the Symmetry

In some cases, you will certainly be inquiry to perform vertical reflections across an axis that symmetry that isn't the y-axis. But before we enter how to deal with this, it's necessary to know what we median by "axis that symmetry". The axis of symmetry is simply the vertical line that we space performing the have fun across. It can be the y-axis, or any vertical line through the equation x = constant, like x = 2, x = -16, etc.

Finding the axis that symmetry, prefer plotting the reflect themselves, is likewise a simple process. In this case, every we need to do is choose the same point on both the role and the reflection, count the distance between them, and divide that by 2. This is because, through it's definition, one axis of symmetry is exactly in the middle of the duty and that reflection.

The best means to exercise finding the axis of the contrary is to do an instance problem:


Find the axis of symmetry because that the 2 functions show in the photo below.

Again, every we need to do to solve this difficulty is to pick the same suggest on both functions, count the distance between them, and divide through 2. Let's pick the origin point for this functions, as it is the easiest allude to deal with.

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Now, by counting the distance between these 2 points, friend should gain the price of 8 units. The last action is to division this value by 2, giving us x = 4 together our axis of symmetry! Let's take it a look in ~ what this would look favor if there were an actual line there:

And that's all there is to it! For more study with revolutions of a attributes with regards come trigonometric functions, check out our class on revolutions of trig graphs and how to find trigonometric functions by graphs.