Exploring transformations and parent graphs
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The document discusses transformations and parent graphs. It defines transformations as changes to the position, size, or shape of a figure. Specific transformations covered include translation, reflection, and stretches/compressions. Translation slides points in a direction, reflection flips points across an axis, and stretches/compressions change point distances from an axis. The document also introduces common parent graphs like linear, quadratic, and cubic functions and states the learning targets are applying transformations and identifying parent graphs.
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The document discusses different types of functions and their graphs. It provides examples of constant functions, linear functions, quadratic functions, and absolute value functions. It shows how to graph each type of function by plotting points and describes their domains and ranges. For linear functions, the domain is all real numbers and the range is also all real numbers. For quadratic functions, the graph is a parabola and the range only includes positive values. Absolute value functions have a domain of all real numbers and a range that is positive and excludes negative values below the constant.
PAIR OF LINEAR EQUATION IN TWO VARIABLE
Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
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CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
This document provides information about linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c. The document also discusses finding the solutions of linear equations, graphing linear equations, and equations of lines parallel to the x-axis and y-axis. Examples are provided to illustrate key concepts. In the summary, key points are restated such as linear equations having infinitely many solutions and the graph of a linear equation being a straight line.
linear equation
1) The document discusses linear equations in two variables, including defining their form as ax + by = c, explaining that they have infinitely many solutions, and noting that their graphs are straight lines.
2) Specific topics covered include finding solutions, drawing graphs, identifying equations for lines parallel to the x-axis and y-axis, and providing examples of writing and solving linear equations.
3) The summary restates the key points about the properties of linear equations in two variables, such as their graphical and algebraic representations.
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Exploring transformations and parent graphs
- 2. Learning Targets • Students will be able to apply and describe transformations • Students will be able to identify parent graphs
- 3. Standards • Building new functions from existing functions o identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. o CCSS.MATH.CONTENT.HSF.BF.B.3
- 4. Image Notice • All images used are either made by me or accessed on google using the labeled for reuse search filter.
- 5. Parent Graphs Constant 𝑦 = 𝑐 Linear 𝑦 = 𝑥 Quadratic 𝑦 = 𝑥2 Constant Cubic 𝑦 = 𝑥3 Square root 𝑦 = 𝑥 Images created by me using Kuta Software
- 6. Transformations: Translation • Transformation: Change in the position, size, or shape of a figure • Translation: slide each point the same distance in the same direction. • Horizontal translations: each point shifts right or left by a number of units • Vertical translation: each point shifts up or down by a number of units • Note: can have both horizontal and vertical translation— for example: three units up and two left
- 7. Transformation: Reflection • Reflection across the y-axis o X coordinate changes, y coordinate stays the same • Reflection across the x-axis o Y coordinate changes, x coordinate stays the same
- 8. Transformation: Stretches and Compression • Horizontal stretch: each point is pulled away from the y- axis o X coordinate changes • Horizontal compression: each point is pushed toward the y-axis o X coordinate changes • Vertical stretch: each point is pulled away from the x-axis o Y coordinate changes • Vertical compression: each point is pushed toward the x- axis o Y coordinate changes