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Unit 1.7 – Graph Linear Functions

Unit 1.7 – Graph Linear Functions. Unit 1 – Algebra: Linear Functions. 1.7 – Graph Linear Functions Georgia Performance Standard: MM1A1a – Represent functions using function notation. MM1A1b – Graph the basic function f(x) = x n

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Unit 1.7 – Graph Linear Functions

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  1. Unit 1.7 – Graph Linear Functions

  2. Unit 1 – Algebra: Linear Functions • 1.7 – Graph Linear Functions • Georgia Performance Standard: • MM1A1a – Represent functions using function notation. • MM1A1b – Graph the basic function f(x) = xn • MM1A1c – Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x and y-axes.

  3. Vocabulary • Function Notation • f(x) = mx + b • Family of functions • Is a group of functions with similar characteristics • Parent linear function • Most basic linear function in the family of all linear functions

  4. What is a function? • So think of…… f(x) = A machine! • When you plug in an x-value, you will get out an f(x)-value. • Input • Output

  5. So what do we do with a function? • A function has to meet one requirement: • Every x-value you plug into it has to produce exactly one output. • In other words, if you plug x = 1 into a function, you’ll never get two different answers.

  6. Example: • What is the value of the function f(x) = -4x -3 when x = -2? • Steps to Solve: • Write original function f(x) = -4x-3 • Substitute -2 for x f(-2)= 4(-2)-3 • Simplify =-3

  7. What if you already know f(x)? • Plug it into the equation and solve! • Example: • For the function f(x) = -4x + 2, find the value of x so that f(x) = -12

  8. Graphing continued… • How do we graph a function? • Same steps as before • Find b & m • What is f(x) = x?? And what can we tell from it? • Shifts (Stretch & Shrink) • Parallel & Perpendicular

  9. Unit 1.8

  10. Unit 1 – Algebra: Linear Functions • 1.8 – Predict with Linear Models • Georgia Performance Standard: • MM1A1d- Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

  11. Vocabulary • Best-fitting line: • The line that most closely follows a trend in data • Zero of a function: • y= f(x) is an x-value for which f(x) = 0

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