![]() Just remember, any time you take a function and you replace its x with a -x, you reflect the graph around the y axis. So as predicted, it's a reflection it's a reflection of our parent graph y equals 2 to the x. But the X-coordinates is transformed into its opposite signs. I have 1 comma one half, I have 0 1, so passes through this point and -1 2. When a point is reflected across the Y-axis, the Y-coordinates remain the same. Now what about y equals 2 to the -x? Let me choose another colour. Formula List Reflect over x-axis (a, b) (a,b) ( a, b) ( a, b) Ex. 1 one half, 0 1 and 1 2 and I've got my recognizable 2 to the x graph that looks like this. And so I'm just going to plot these two functions. But if -x=u then really I just have the 2 to the u values here so these values just get copied over. So -1 becomes 1, 0 stays the same and 1 becomes -1. So if I let u equal -x and x=-u and all I have to do is change the sign of these values. So those are nice and easy and then to make the transformation, I'm going to make the change of variables -x=u. 2 to the negative 1 is a half, 2 to the 0 is 1, 2 to the 1 is 2. A function reflection is the graph of the original function, but where the graph has been flipped upside-down (that is, where it has been reflected in the x. I'm going to change variables to make it easier to transform and I'm going to pick easy values of u like -1 0 and 1 to evaluate 2 to the u. We call the y equals 2 to the x is one of our parent functions and has this shape sort of an upward sweeping curve passes through the point 0 1, and it's got a horizontal asymptote on the x axis y=0. So I want to graph y equals 2 to the x and y equals y equals 2 to the -x together. Now to see this, let's graph the two of them together. This is a reflection of what parent function? Well it's y equals to the x right? This will be a reflection of y equals to the x. So let's consider an example y=2 to the negative x. So you replace the x with minus x and that will reflect the graph across the y axis. Since the reflection applied is going to be over the x-axis, that means negating the y-value. ![]() But how do you reflect it across the y axis? Well instead of flipping the y values, you want to flip the x values. Determine the coordinate points of the image after a reflection over the x-axis. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right. Reflections create mirror images of points, keeping the same distance from the line. All you have to do is put a minus sign in front of the f of x right? Y=-f of x flips the graph across the x axis. We can plot points after reflecting them across a line, like the x-axis or y-axis. Now recall how to reflect the graph y=f of x across the x axis.
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