Today I am going to teach you about transformations. By changing the parent function of a graph, you can alter the way in which the graph appears or moves on the grid.
Let's start with the function notation for a basic quadratic graph: f(x) = x2. A function transformation takes whatever f(x) is and then transforms it. For example, three units higher than the quadratic parent function, F(x) = x^2, is x^2 + 3. By simply adding a 3 to the outside, you shift the parabola up 3 units along the y-axis from it's original starting location.
Lets take a look at another transformational function F(x)=(x+3)^2. With this you see the graph shifted 3 units to the left. This is because whenever a number is placed inside the function argument, it is shifted along the x-axis. So if a number is added in the argument it shift left along the x-axis, but if a number is subtracted in the argument, it is shifted to the right along the x-axis.
The last transformation function I am going to look at is f(x)=-x^2. When you do this you simply reflect the graph on the x-axis. When we take a look at the function G(-x)=-x^3. this graph is a reflection on the y-axis. So -f(x) is a reflection about the x-axis and g(-x) is a reflection about the y-axis.
This is a great overview of transformation that is easy to understand and well organized. Personally, transformations are the bane of my existence. I don't get them. I don't like them. But this helped. Thanks!
ReplyDeleteI thought this was a really good explanation of transformations. It's short and sweet and it gets its point across. The explanation is really well done.
ReplyDeleteThis was a great explanation of transformations. It told me what I needed to know and quickly. Good work!
ReplyDeletecooper,
ReplyDeletevery nicely explained, but definitely could have used some visual examples (like graphs) so that your audience can see how the graph looks after it's transformed.
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