![]() ![]() Drag points A, B, and C to see how a reflection over the y-axis impacts the image. Now because the inverse of the mapping $x \mapsto 2x$ is $x \mapsto \frac$, then scaling $y$ coordinates by $A$, then shifting up by $D$ makes sense. On this page, we will practice drawing the axis on a graph, learning the formula, stating the equation of the axis of symmetry when we know the parabolas. Explore math with our beautiful, free online graphing calculator. On the other hand say we perform $x \mapsto 2x$, now we have $y-f(2x)=0$. You might expect the graph to be composed of points $(x+1,y)$ with respect to the old graph, but this is not true rather it is composed of points $(x-1,y)$, i.e. The triangle shown above has the following vertices: A ( 1, 1), B ( 1, 2), and C ( 4, 2). Apply what has been discussed to reflect A B C with respect to the line y x. ![]() If you consider $f(x,y)=y-f(x)=0$ then for every substitution you perform you'll witness an inverse mapping in the graph.įor example say we perform $x \mapsto x+1$, so now we have $y-f(x+1)=0$. The best way to master the process of reflecting the line, y x, is by working out different examples and situations. ![]() This graph is a set $G$ consisting of points $(x,y)$ where $x$ is in the domain of the function. Let's say you have some function $y=f(x)$, it has some graph. In order to understand what works and what doesn't work you need to understand what's going on. Solution : Step 1 : Since we do reflection transformation across the y-axis, we have to replace x by -x in the given function y x Step 2 : So, the formula that gives the requested transformation is y -x Step 3 : The graph y -x can be obtained by reflecting the graph of y x across the y-axis using the rule given below. Can be thought of taking $f(x)=y$ and performing the following substitution. ![]()
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