Shifting, stretching and reflecting parent function graphs. Summary of graphs of parent functions page 42 sketch an example of each of the six most commonly used functions in algebra. Shifting, reflecting, and stretching graphs vertical shifts horizontal shifts reflecting stretching and flattening. Theory of shifting, reflecting and stretching graphs. Write the word or phrase that best completes each statement or answers the question. If a 1, we say the graph of f has undergone a vertical stretching expansion, dilation.
Scale a translation in which the size and shape of the graph of a function is changed. Graphical transformations of functions miami arts charter school. Many functions have graphs that are simple transformations of the graphs of parent functions. Determine the intervals on which the function is increasing, decreasing, and constant. Professor elviszap teaches you how to stretch shift and reflect the graph of a square root. We will examine four basic functions and the parent graphs associated with each.
If gxfxc, where c0 then the value of g at x is the same as the value of f at xc c units to the left of x. Vertical and horizontal shifts in the graph of y fx and represented as follows. The graphs of many functions are transformations of the graphs of very basic functions. Stretching, shrinking, and reflecting graphs short answer. Stretching, compressing, or reflecting an exponential. Most graphs of functions can be made by transforming shifting, stretching, shrinking, reflecting or combining these common graphs. A rigid transformation is a transformation in which the basic shape of the graph is unchanged.
Shift graphs left, right, up, down reflect graphs across the x or y axis stretch graphs or shrink you may also look at a graph and be asked to explain what happened to the original graph. Summary of graphs of parent functions page 42 sketch an example of each of the six most commonly used functions in. You can identify a ytransformation as changes are made outside the brackets of yf x. 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. Recognize graphs of parent functions use vertical and horizontal shifts to graph functions use reflection to graph functions use nonrigid transformations to graph functions. It is a translation in which the shape and size of a graph of a function is not modified, however the position of the graph is. Shifting, reflecting, and stretching graphs monday, august 29, 2011 goals.
In other words, a function is reflected with respect to the xaxis by multiplying the entire function by. Shifting, reflecting, and stretching graphs notes jason. Functions stretching, compressing, and reflecting functions. A square root function is the opposite of a squared function. Lesson 3a shifting, reflecting, shrinking, and stretching. We have already had experience with constant and linear functions, and have been introduced, albeit sparingly, to the other graphs. Vertical and horizontal shifts let c be a positive real number. Reflection over xaxishorizontal shift right 3 unitsvertical shift downward 2 units 33.
Shifting up or down vertical shifting left or right horizontal reflecting in the yaxis horizontal reflecting in the xaxis vertical vertical stretchingshrinking vertical horizontal stretchingshrinking horizontal a summary of the results from examples 1 through 6 are below, along with whether or. Stretching and compressing graphs vertically is determined by the coefficient in front of the x or more specifically, in front of the other direct modifications to x. Let f x x describe the graph of gx x in terms of f. Shifting, reflecting, and stretching graphs vertical shifts horizontal shifts reflecting stretching and flattening most typically transformed graphs page 42.
Nevertheless, these are very common functions and it is. Calculus 1 functions in this video, we learn an algebraic way to stretch, compress, and reflect the graphs of functions. Vertical translations a shift may be referred to as a translation. Finally, take the last graph and shift 1 unit le ft and 3 units down to complete the graph. These functions are y x, y x2, 3, y x, y x and x y 1. Before we define translating and reflecting mathematically we need to know the graphs of six basic functions. Shifting, flipping, stretching, and missouri western state. Lesson 3a shifting, reflecting, shrinking, and stretching graphs.
It is a translation in which the shape and size of the graph of. I chose to focus on the first only, suggesting how the student could discover what a. Shifting, reflecting and stretching graphs part 1 section 1. You start with ysquare root of x1 it becomes 0 reflecting and stretching section objectives. The graph of y x2 is the reflection of the graph of y x2 in the xaxis. Shifting up or down vertical shifting left or right horizontal reflecting in the yaxis horizontal reflecting in the xaxis vertical vertical stretching shrinking vertical horizontal stretching shrinking horizontal a summary of the results from examples 1 through 6 are below, along with whether or. Vertical and horizontal shifts in the graphs of y fx are represented as follows. A ytransformation affects the y coordinates of a curve. In function notation, h and f are related as follows. The x coordinates are unaffected but all the y coordinates go up by 4. By reflecting the graph of f across the yaxis, we obtain the graph of y fx.
Now, to vertically compress this curve, you put a fraction coefficient in front of the x component of. In addition to shifting, compressing, and stretching a graph, we can also reflect it about the xaxis or the yaxis. Really clear math lessons prealgebra, algebra, precalculus, cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. The graph of g is a reflection of the graph of f in the xaxis. Notes,whiteboard,whiteboard page,notebook software,notebook, pdf,smart,smart technologies inc,smart board interactive whiteboard created date.
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. Students will recognize graphs of common functions, use vertical and horizontal shifts and reflections to sketch graphs of functions, and use nonrigid transformations to sketch a graph. When we multiply the input by 1, we get a reflection about the yaxis. Conversely, students will be able to create graphs from basic functions using the. We should always take care of the stretching or shrinking and reflections first. When we multiply the parent function latexf\leftx\rightbxlatex by 1, we get a reflection about the xaxis. Start by graphing y 2x by plotting at least 3 points.
In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions. Sketch the graphs of the three functions by hand on the same rectangular coordinate system. 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. It is a translation in which the shape and size of a graph of a function is not modified, however the position of the graph is scale. Stretches compressions translations shifts reflections chandler. Jan 07, 2019 translating functions explain how the following graphs are obtained from the graph of y fx. Basic definitions of shifting, reflecting and stretching graphs. Shifting reflecting and stretching graphs activity. Shifting, stretching, shrinking, and reflecting of graphs example. Activity 4 graph each of the functions on the same graph. Find the vertex, direction of the opening, and transformations of the quadratic equation.
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