Thought of how far to go in the x-direction (an x-scaling) and the "b" couldįar to go in the "y" direction (a y-scaling).
Where a was the x-intercept and b was the y-intercept of the line.
#REFLECTION RULES SERIES#
Trigonometry (Math 117) and Calculus (Math 121, 122, 221, or 190).Įarlier in the text (section 1.2, problems 61-64), there were a series of problems which wrote the Understanding the concepts here are fundamental to understanding polynomial and rationalįunctions (ch 3) and especially conic sections (ch 8).
Putting it all togetherĬonsider the basic graph of the function: y = f(x)Īll of the translations can be expressed in the form: To reflect about the x-axis, multiply f(x) by -1 to get -f(x). To reflect about the y-axis, multiply every x by -1 to get -x. ReflectionsĪ function can be reflected about an axis by multiplying by negative one. With the x, then it is a horizontal scaling, otherwise it is a vertical scaling. Scaling factors are multiplied/divided by the x or f(x) components. The vertical and horizontal scalings can be
A horizontal scaling multiplies/divides every x-coordinate by aĬonstant while leaving the y-coordinate unchanged. A vertical scaling multiplies/divides every y-coordinate by a constant while leaving A scale will multiply/divide coordinates and this will change the appearance as well as Scales (Stretch/Compress)Ī scale is a non-rigid translation in that it does alter the shape and size of the graph of theįunction. Then it is a horizontal shift, otherwise it is a vertical shift. Shifts are added/subtracted to the x or f(x) components. Vertical and horizontal shifts can be combined into one expression. A vertical shiftĪdds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.Ī horizontal shift adds/subtracts a constant to/from every x-coordinate while leaving the y-coordinate unchanged. All that a shift will do is change the location of the graph. There are three if you count reflections, but reflections are just a special case of theĪ shift is a rigid translation in that it does not change the shape or size of the graph of theįunction. There are two kinds of translations that we can do to a graph of a function. Your text calls the linear function the identity function and the quadratic function the squaring Greatest Integer Function: y = int(x) was talked about in the last section.These are the common functions you should know the graphs of at this time: Sketch a new function without having to resort to plotting points. Understanding these translations will allow us to quickly recognize and New graph as a small variation in an old one, not as a completely different graph that we have Understanding the basic graphs and the way translations apply to them, we will recognize each Graphs, we are able to obtain new graphs that still have all the properties of the old ones. There are some basic graphs that we have seen before. Mathematics presented to you without making the connection to other parts, you will 1) becomeįrustrated at math and 2) not really understand math. Which makes comprehension of mathematics possible. You can understand the foundations, then you can apply new elements to old. Part of the beauty of mathematics is that almost everything builds upon something else, and if Reflection A translation in which the graph of a function is mirrored about an axis. Scale A translation in which the size and shape of the graph of a function is changed. 1.5 - Shifting, Reflecting, and Stretching Graphs 1.5 - Shifting, Reflecting, and Stretching Graphs Definitions Abscissa The x-coordinate Ordinate The y-coordinate Shift A translation in which the size and shape of a graph of a function is not changed, but
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