![]() 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. I have 1 comma one half, I have 0 1, so passes through this point and -1 2. Now what about y equals 2 to the -x? Let me choose another colour. ![]() 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. 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. But how do you reflect it across the y axis? Well instead of flipping the y values, you want to flip the x values. 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. Now recall how to reflect the graph y=f of x across the x axis. Images/mathematical drawings are created with GeoGebra.Let's talk about reflections. When the square is reflected over the line of reflection $y =x$, what are the vertices of the new square?Ī. Suppose that the point $(-4, -5)$ is reflected over the line of reflection $y =x$, what is the resulting image’s new coordinate?Ģ.The square $ABCD$ has the following vertices: $A=(2, 0)$, $B=(2,-2)$, $C=(4, -2)$, and $D=(4, 0)$. Use the coordinates to graph each square - the image is going to look like the pre-image but flipped over the diagonal (or $y = x$). This means that the image of the square has the following vertices: $A=(3, -3)$, $B=(1, -3)$, $C=(1, -1)$, and $D=(3, -1)$. WolframAlpha brings expert-level knowledge and capabilities to the broadest possible range of peoplespanning all professions and education levels. A vertical reflection reflects a graph vertically across the. ![]() To reflect $\Delta ABC$ over the line $y = x$, switch the $x$ and $y$ coordinates of all three vertices. Another transformation that can be applied to a function is a reflection over the x or y-axis. The triangle shown above has the following vertices: $A = (1, 1)$, $B = (1, -2)$, and $C = (4, -2)$. Read more How to Find the Volume of the Composite Solid?
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