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 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. You must use positive angles or CW or negative angles for CCW. If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located. This calculator will tell you its (0,-1) when you rotate by +90 deg and (0,1) when rotated by -90 deg. Reflect over the x-axis: When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). The vector (1,0) rotated +90 deg CCW is (0,1). 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 X,Y equations listed are for CW rotations but the calculator tells you to define CCW as positive. 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. The graph of this function is in green, while the graph of the original function is in purple. The transformed function equation would look like: f (x) (x+1)3. Can be thought of taking $f(x)=y$ and performing the following substitution. If we wanted to reflect this graph over the y-axis, we would keep all of the y-coordinates the same, but the signs on the x-values would be flipped.
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