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Introduction to Linear Functions

Introduction to Linear Functions. What did we learn about functions?. We spent the last unit discussing functions. We found the independent variable , __ , the dependent variable , __,

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Introduction to Linear Functions

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  1. Introduction to Linear Functions

  2. What did we learn about functions? We spent the last unit discussing functions. We found the independent variable, __, the dependent variable, __, the __________, the ______, and the ________for the function. This unit we will be looking at a specific type of function – ___________________. x y equation table graph Linear Functions

  3. Similarties FunctionsLinear Functions Differences: Both have tables. Both have graphs. Both have equations. Both have a domain and range Both have independentand dependent variables. Both can be continuous, the data is connected. Functions can be discrete, the data is not connected.

  4. What does a Linear Function look like on a graph? A ________ __________ is a function that on a graph the solutions, ______, are represented by a _________ linear function (x,y) line.

  5. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is not a line. It is a nonlinear function. Yes, it is a function. The graph is a line. It is a linear function.

  6. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.

  7. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. No, not a function.

  8. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is not a line. It is a nonlinear function. No, not a function.

  9. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is not a line. It is a nonlinear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.

  10. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. No, not a function.

  11. Examples of functions: Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.

  12. Vocabulary for linear functions • Linear function – function with a graph that is continuous • Linear equation – equation whose graph is a straight line • X intercept – the point where a line crosses the x axis of a graph • Y intercept – the point where a line crosses the y axis • Rate of change – how the steepness of a line is changing • Slope – the steepness of the line on a graph

  13. Slope formula – the formula used to find the slope between two ordered pairs • Slope intercept form – y = mx + b – a form used to graph linear functions • Point slope from – y – y1 = m(x – x1) • Domain – the list of all x values • Range – the list of all y values • Independent variable – the input you choose for x • Dependent variable – the output you get when you choose the input and apply the function rule

  14. Function rule – the rule that defines the relationship between x and y

  15. Function rule – the rule that defines the relationship between x and y • Positive slope – the line on a graph moves in an upward direction from left to right

  16. Function rule – the rule that defines the relationship between x and y • Positive slope – the line on a graph moves in an upward direction from left to right • Negative slope – the line on a graph moves in a downward graph from left to right

  17. Function rule – the rule that defines the relationship between x and y • Positive slope – the line on a graph moves in an upward direction from left to right • Negative slope – the line on a graph moves in a downward graph from left to right • Zero slope – the slope of a horizontal line

  18. Function rule – the rule that defines the relationship between x and y • Positive slope – the line on a graph moves in an upward direction from left to right • Negative slope – the line on a graph moves in a downward graph from left to right • Zero slope – the slope of a horizontal line • Undefined slope – the slope of a vertical line

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