Another transformation that can be applied to a function is a reflection over the x or y axis. Solution because the graph is a transformation of the graph of y 2cos 2 3 x. For example, this figure shows the parent function f x x2 and the reflection g x 1 x2. Functions, relations, and transformations 4 overview in discovering advanced algebra, students study mathematical functions modeling realworld problems. Shifting, reflecting, and stretching graphs vertical shifts horizontal shifts reflecting stretching and flattening most typically transformed graphs page 42.
These functions are y x, y x2, 3, y x, y x and x y 1. When we multiply the input by 1, we get a reflection about the yaxis. Mathematics this mep text book for year 9 students covers graphs, equations and inequalities. Stretching, compressing, or reflecting an exponential function. Functions stretching, compressing, and reflecting functions. It contains a number of exercises that look at linear. In this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. The set of input values is the and the set of output values is the a relation is a provided there is exactly one output for each input. Calculus 1 functions in this video, we learn an algebraic way to stretch, compress, and reflect the graphs of functions.
Another type of transformation is called a reflection. Graph transformations about the xaxis and yaxis rotate to landscape screen format on a mobile phone or small tablet to use the. Shifting, reflecting, and stretching graphs notes jason. I use the exit slip as a quick formative assessment to check for each students understanding of evaluating a function from a graph using function notation. Graphing basic functions via shifting and reflecting by jon blakely. If k reflecting, and stretching graphs vertical shifts horizontal shifts reflecting stretching and flattening most typically transformed graphs page 42. Writing graphs as functions in the form is useful when applying translations and reflections to graphs.
Recognize graphs of parent functions use vertical and horizontal shifts to graph functions use reflection to graph functions use. Graphical transformations of functions in this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. Analogies abound with numbertheoretic functions such as riemann or dedekind zeta functions. Scale a translation in which the size and shape of the graph of a function is changed. Summary of graphs of parent functions sketch an example of each of the six most commonly used. In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions. Summary of graphs of common functions page 100 sketch an example of each of the six most commonly used functions in algebra. Independent practiceevaluating functions using a graph. Students are to complete the exit slips on their own without assistance from their table partner or me. Both graphs are shown below to emphasize the difference in the final results but we can see that the above functions are different without graphing the functions. We can use the following rules to graph reflecting functions over the x and y axes. A point x, y ony fx corresponds to the point x, y on the graph of y is the image of. In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions i. I give the students the exit slip about 10 minutes before the end of class.
Really clear math lessons prealgebra, algebra, precalculus, cool math games, online. Shifting, reflecting and stretching graphs we begin this lesson with a summary of common graphs that we have seen thus far. We have already had experience with constant and linear functions, and have. Practice this relationship between the graphical and algebraic.
Really clear math lessons prealgebra, algebra, precalculus, cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. Sep 29, 2016 learn how to recognize shifts, vertical and horizontal stretches and reflections as they affect parent functions in this free math video tutorial by marios math tutoring. Vertical translations a shift may be referred to as a translation. To recognize graphs of common functions to use vertical and horizontal shifts and reflections to graph functions to use nonrigid transformations to graph functions title. Summary of graphs of parent functions page 42 sketch an example of each of the six most commonly used functions in algebra. How to reflect a graph through the xaxis, yaxis or origin. Zeta functions of graphs graph theory meets number theory in this stimulating book. In the previous section we talked about graphing functions. That is, if we reflect an even function in the yaxis, it will look exactly like the original. When we multiply the parent function latexf\leftx\rightbxlatex by 1, we get a reflection about the xaxis. Summary of transformations to graph draw the graph of f and. Translating graphs transformation of curves bbc bitesize. To recognize graphs of common functions to use vertical and horizontal shifts and reflections to graph functions to use. What are the key features of the graphs of the sine and cosine functions.
A vertical reflection reflects a graph vertically across the x axis, while a horizontal reflection reflects a graph. Here, the abstract idea of a function grows out of students earlier experiences with linear equations and graphing. In addition to shifting, compressing, and stretching a graph, we can also reflect it about the xaxis or the yaxis. C d write the equation of a sine function that has the given characteristics. Nevertheless, these are very common functions and it is. We have already had experience with constant and linear functions, and have been introduced, albeit sparingly, to the other graphs. In this lesson, you will learn about the three basic. Learn how to recognize shifts, vertical and horizontal stretches and reflections as they affect parent functions in this free math video tutorial by marios math tutoring. In this lesson you learned how to identify and graph shifts, reflections, and nonrigid. In previous sections, we learned the graphs of some basic functions. Shifting, reflecting, and stretching graphs monday, august 29, 2011 goals. Stretching, compressing, or reflecting an exponential. Similarly, f 2x x 2 is just the basic graph flipped over and moved up two units.
But sometimes, the reflection is the same as the original graph. How to recognize graphs of parent functions section 1. Shifting, reflecting, and stretching graphs vertical shifts horizontal shifts. For example, if we begin by graphing the parent function latex. Recognize graphs of parent functions use vertical and horizontal shifts to graph functions use reflection to graph functions use nonrigid transformations to graph functions. Reflecting functions are functions whose graphs are reflections of each other. It contains a number of exercises that look at linear inequalities on a number line, solving linear inequalities, a recap of the equation of a straight line, graphs of quadratic functions, plotting quadratics using a table, translating quadratic graphs.
You can move the graph of a linear function around the coordinate grid using transformations. Reflections occur when either the input or the output of a function is mul tiplied by. Collectively, these are known as the graphs of the. The graph of y x2 is the reflection of the graph of y x2 in the xaxis. If you find the value of both functions at the same number. Transformations of functions alamo colleges district. Graphs a function is often used to describe phenomena in fields such as science, engineering. An alternative way to graphing a function by plotting individual points is to perform transformations to the graph of a function you already know.
We saw that the graph of f x 2 x 2 is just the basic graph f x 2 moved over to the right two units. The graphs of many functions are transformations of the graphs of very basic functions. The graph of ykx is the graph of yx scaled by a factor of k. Shifting, stretching and reflecting parent function graphs. Transformations of functions, horizontal and vertical reflections. Solution because the graph is a transformation of the graph of y 2cos 2 3 x, the amplitude is 2 and the period is 3 by comparing the given equation to the general equation yacosbx.
Reflecting functions or graphs with worksheets, videos. When we multiply the parent function latexf\leftx\rightbxlatex. Another way of rigidly transforming a graph of a function is by a reflection in a coordinate axis. This is when the graph is shifted across the x or yaxis. A vertical reflection reflects a graph vertically across the x axis, while a horizontal reflection reflects a graph horizontally across the y axis. Exponential functions notes 3 asymptotes an asymptote is a line that an exponential graph gets closer and closer to but never touches or crosses.