Graph transformations cheat sheet
How do you graph a function with more than one transformation?
If a function contains more than one transformation it may be graphed using the following procedure: Use the following order to graph a function involving more than one transformation: 1. Horizontal Translation 2. Stretching or shrinking 3.
What is vertical translation of a graph?
In general, a vertical translation means that every point (x, y) on the graph of is transformed to (x, y + c) or (x, y – c) on the graphs of or – respectively. If c is added to the variable of the function, where the function becomes , then the graph of will horizontally shift to the left c units.
What happens to the graph when the function becomes and/or stretches?
So when the function becomes and , a vertical shrinking of the graph of will occur. Graphically, a vertical shrinking pulls the graph of toward the x-axis. When in the function , a vertical stretching of the graph of will occur. A vertical stretching pushes the graph of away from the x-axis.
How do you graph X and Y values?
Steps: 1:set inside = to zero. 2:solve for x. 3:create a table with the found x value in the middle. 4:Plug x back into the equation to find y. (This is the vertex coordinate.) 5:choose 2 more x values, one on either side of the x you found. 6:Find y values. 7:Graph 3 points. Example: Graph y = |x + 5| (Absolute Value)
2-4 Transformations of Absolute Value Functions
When a function has a vertex, the letters h and k are used to represent the coordinates of the vertex. Because an absolute value function has a vertex, the general form is y = a0x-h0 + k.The vertical stretch or compression factor is 0a 0, the vertex is located at (h, k), and the axis of symmetry is the line x = h.Key Concept General Form of the Absolute Value Function
[PDF File]Data Visualization with ggplot2 : : CHEAT SHEET
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Data Visualization with ggplot2 : : CHEAT SHEET ggplot2 is based on the grammar of graphics, the idea that you can build every graph from the same components: a data set, a coordinate system, and geoms—visual marks that represent data points.
[PDF File]Function Parent Graph Characteristics Name Function
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“Cheat Sheet” 6 November 2019 Function Name Parent Function Graph Characteristics Algebra Constant ( T)= Domain: (− ∞, ) Range: [c, c] Inverse Function: Undefined (asymptote) Restrictions: c is a real number Odd/Even: Even General Form: + =0 Linear or = Identity ( T) T Domain: (−∞, ∞) Range: (−∞, ∞)
[PDF File]Vertical and Horizontal Shifts of Graphs
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SECTION 1.3 Transformations of Graphs MATH 1330 Precalculus 87 Looking for a Pattern – When Does the Order of Transformations Matter? When deciding whether the order of the transformations matters, it helps to think about whether a transformation affects the graph vertically (i.e. changes the y-values) or horizontally (i.e. changes the x-values).
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Graphing Absolute Value equations (Cheat Sheet) Steps: 1: set inside = to zero. 2: solve for x. 3: create a table with the found x value in the middle. 4: Plug x back into the equation to find y. (This is the vertex coordinate.) 5: choose 2 more x values, one on either side of the x you found. 6: Find y values. 7: Graph 3 points. Example: Graph y = |x + 5| (Absolute Value)
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Graph for: y > -1/2x + 1 1. Graph y = -1/2x + 1, but dot the line since the symbol is >. The points on the line are not solutions. 2. Pick a point such as (0,0) and substitute it into the inequality. (0,0) is not a solution, therefore, shade the side of the line that does not contain (0,0). Special Rule - Just for Inequalities
[PDF File]Graph Transformations - University of Utah
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Transformations “after” the original function Suppose you know what the graph of a function f(x) looks like. Suppose d 2 R is some number that is greater than 0, and you are asked to graph the function f(x)+d. The graph of the new function is easy to describe: just take every point in the graph of f(x), and move it up a distance of d. That
[PDF File]Graphing Standard Function & Transformations
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The graph of y = f (-x) is the graph of y = f (x) reflected about the y-axis. Here is a picture of the graph of g(x) =(0.5x)3+1. It is obtained from the graph of f(x) = 0.5x3+1 by reflecting it in the y-axis. Summary of Transformations To graph Draw the graph of f and: Changes in the equation of y …
[PDF File]2. Graphical Transformations of Functions
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A vertical stretching pushes the graph of away from the x-axis. In general, a vertical stretching or shrinking means that every point (x, y) on the graph of is transformed to (x, cy) on the graph of . 𝑓 Horizontal Stretching and Shrinking If c is multiplied to the …
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Transformations of graphs: A. is the graph of shifted horizontally units (to the right if and to the left if ) B. is the graph of shifted vertically units (up if and down if ) C. is the graph of stretched or shrunk vertically by a factor of (stretched if and shrunk if ) D. is the graph …
[DOC File]Graphing Linear Equations – Table of Values
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Complete the table for and graph the resulting line. x. y Sheet # 15-03 Name: _____ Date: _____ Functions and Relations – Graphing using a table of values Class: Pre-Algebra. Complete the table for and graph the resulting line. x. y-4 -2 . 0 . 2 . 4 . Complete the table for and graph the resulting line. ...
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In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State S
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Label this graph n(x). Write its equation here: _____ Graph y = h(x) after it has been translated down 3 units and then reflected over the x-axis. Label this graph q(x). Write its equation here: _____. How does it compare to n(x)? Worksheet #6. The following graph tells a story. Write a story that would model this graph.
[DOC File]Math 052 - Elementary Algebra - Oakton Community College
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2. Identify and apply transformations of graphs. 3. Solve linear and non-linear equations, and systems of two equations. 4. Solve polynomial and rational inequalities algebraically and graphically. 5. Sketch the graph of polynomials using zeros and end behavior. 6. Sketch the graph of rational functions using zeros, asymptotes, and end behavior. 7.
[DOCX File]Grade 8
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How can you evaluate and graph functions and their transformations? Objectives: Students will: Sketch the graph of an equation. Find the intercepts of a graph. ... Algebra Cheat Sheet. Trigonometry Cheat Sheet. Online Algebra and Trigonometry Tutorial. Study Tips for Math Courses. Literacy.
[DOC File]Transformation Review Sheet:
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b) Graph and state the coordinates of ΔA’B’C’, the image of ΔABC after rx-axis. c) Graph and state the coordinates of ΔA’’B’’C’’, the image of ΔA’B’C’ after T0,-7. d) Which of the above transformations is an example of a direct isometry? 15) Graph each of the following lines: a) y = -9x + 8 b) 2x – 3y = 9
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