Tech teach
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Tech Teach is about how teachers can use technology in the classroom. It discusses both traditional, older teaching methods and newer technologies that teachers can now utilize. The document seems focused on providing teachers guidance on integrating different technologies into their lessons and practices.
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5.1 indentifying linear equations
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- Applications word problems are presented where the domain and range may be restricted based on real-world constraints.
5.3 rate of change
This document provides examples and explanations for calculating rates of change, slopes, and describing slopes of lines based on data points or graphs. It includes examples of finding the rate of change and slope from tables of data, graphs, and lines with positive, negative, zero, or undefined slopes. Students are asked to identify rates of change, calculate slopes, and describe the slope in different examples and practice problems.
4 4 graphingfx
This lesson discusses graphing functions. It begins with examples of graphing functions given a limited domain by finding the y-values that correspond to the given x-values. It then covers graphing functions with an unlimited domain by choosing sample x-values and connecting the points with a line or curve. The document provides examples of interpreting graphs to find function values and solving real-world word problems by graphing and interpreting functions.
How to graph Functions
This lesson discusses graphing functions. It begins with examples of graphing functions given a limited domain by finding ordered pairs that satisfy the function and plotting the points. It then covers graphing functions with a domain of all real numbers by choosing values of x, finding corresponding y-values, plotting points to see a pattern, and drawing a line with arrowheads. The lesson shows how to use graphs to find function values and solve real-world problems by limiting domains to non-negative values.
Functions
A function is a relation where each element of the domain is paired with exactly one element of the range. The key characteristics are that there is one and only one output for each input. Some examples are provided to demonstrate determining if a relation represents a function based on this definition. The vertical line test is also introduced as a visual way to determine if a graph depicts a function. Finally, examples are given of evaluating functions for given inputs using function notation.
PPt on Functions
1. A function is a relation where each input is paired with exactly one output.
2. To determine if a relation is a function, use the vertical line test - if any vertical line intersects more than one point, it is not a function.
3. To find the value of a function, substitute the given value for x into the function equation and simplify.
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Slope
Slope describes the steepness of a line, with a positive slope indicating a line going up from left to right and a negative slope a line going down. Slope is calculated by finding the change in the vertical distance over the change in the horizontal distance between two points on the line, using the formula m=(change in y)/(change in x). Horizontal lines have a slope of zero while vertical lines have no definable slope.
Slope intercept
This document provides a lesson on writing and graphing linear equations in slope-intercept form. It begins with examples of finding the slope and y-intercept of lines and writing the equations in the form y = mx + b. Then it shows how to graph lines from their equations in slope-intercept form. Applications include writing cost functions from word problems and finding values of the functions. A quiz reviews writing equations from slopes and points and graphing lines from their equations.
Slope formula
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5.2 using intercepts
This document provides examples and explanations for finding the x- and y-intercepts of linear equations and using intercepts to graph lines. It defines x- and y-intercepts, shows how to find them by setting variables equal to 0 in the equation, and explains that intercepts represent important values when graphing real-world situations. Examples demonstrate finding intercepts, generating ordered pairs, and graphing lines by plotting the intercept points.
5.2 using intercepts
This document provides examples and explanations for finding the x- and y-intercepts of linear equations and using intercepts to graph lines. It defines x- and y-intercepts, shows how to find them by setting x or y equal to 0, and explains that intercepts represent important values on the graph like when distance or time is 0. Examples demonstrate finding intercepts, generating points, and graphing lines based on the intercepts.
5.1 indentifying linear equations
- The document is a lesson on identifying and graphing linear functions. It provides examples of determining if a graph or set of ordered pairs represents a linear function based on whether a constant change in the x-value results in a constant change in the y-value.
- It also gives examples of writing functions in standard form (y=mx+b) to identify if they are linear and how to graph linear functions by choosing x-values and finding the corresponding y-values.
- Applications word problems are presented where the domain and range may be restricted based on real-world constraints.
5.3 rate of change
This document provides examples and explanations for calculating rates of change, slopes, and describing slopes of lines based on data points or graphs. It includes examples of finding the rate of change and slope from tables of data, graphs, and lines with positive, negative, zero, or undefined slopes. Students are asked to identify rates of change, calculate slopes, and describe the slope in different examples and practice problems.
4 4 graphingfx
This lesson discusses graphing functions. It begins with examples of graphing functions given a limited domain by finding the y-values that correspond to the given x-values. It then covers graphing functions with an unlimited domain by choosing sample x-values and connecting the points with a line or curve. The document provides examples of interpreting graphs to find function values and solving real-world word problems by graphing and interpreting functions.
How to graph Functions
This lesson discusses graphing functions. It begins with examples of graphing functions given a limited domain by finding ordered pairs that satisfy the function and plotting the points. It then covers graphing functions with a domain of all real numbers by choosing values of x, finding corresponding y-values, plotting points to see a pattern, and drawing a line with arrowheads. The lesson shows how to use graphs to find function values and solve real-world problems by limiting domains to non-negative values.
Functions
A function is a relation where each element of the domain is paired with exactly one element of the range. The key characteristics are that there is one and only one output for each input. Some examples are provided to demonstrate determining if a relation represents a function based on this definition. The vertical line test is also introduced as a visual way to determine if a graph depicts a function. Finally, examples are given of evaluating functions for given inputs using function notation.
PPt on Functions
1. A function is a relation where each input is paired with exactly one output.
2. To determine if a relation is a function, use the vertical line test - if any vertical line intersects more than one point, it is not a function.
3. To find the value of a function, substitute the given value for x into the function equation and simplify.
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