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Writing Linear Equations

Bell Work: We are starting a new thing called Bell Work . You need to have your math note books out and start on your bell work when you get seated. This is your daily 5 points. 2 points : No talking and starting on your bell work like asked

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Writing Linear Equations

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  1. Bell Work: We are starting a new thing called Bell Work. You need to have your math note books out and start on your bell work when you get seated. This is your daily 5 points. 2 points: No talking and starting on your bell work like asked 2 points: Showing work and explaining your answer 1 point: correct answer Writing Linear Equations Review

  2. Bell Work • Do you recall working on Linear Equations? When given the equation y = 3x + 5 in the slope-intercept form of y = mx+b, state the slope and the y-intercept of this equation. Hint: m = slope b = y-intercept When you are done quietly sit, I will come check your answer and work.

  3. Let’s Review • Slope-intercept form is y = mx + b • Where m represents the slope of the line and b represents the y-intercept. • Therefore, write an equation of the line with a slope of -2 and a y-intercept of 5.

  4. Review Which equation represents the line shown? Why? Y = x +5 Y = -x +5 Y = x -5 Y= -x +5

  5. Function Notation •  While parentheses have, up until now, always indicated multiplication, the parentheses do not indicate multiplication in function notation. • The expression "f(x)" means "plug a value for x into a formula f “ • The expression does not mean "multiply f and x"! Don't embarrass yourself by pronouncing (or thinking of) "f(x)" as being "f times x".

  6. Function Notation: the "x" in "f(x)" is called "the argument of the function", or just "the argument". So if they give you "f(2)" and ask for the "argument", the answer is just "2". Let’s Practice: F(3) = F(4) = F (1233232) =

  7. Practice • Given  f(x) = x2 + 2x – 1, find  f(2). • Step 1: You are finding the function of 2. So, you can re-write the equation as f(2) = x2 + 2x – 1. This way you know you are plugging in 2 for your unknown. • Step 2: Plug in argument (2) in for the unknown, in case “x”.   f(2) = 22 + 2(2) – 1

  8. Step 3: Solve by using PEMDAS. (Matt’s favorite word) Always start your answer as the function of “the given number” = f(2) = 22 + 2(2) – 1 = f (2) = 4 + 4 – 1 = Answer : f(2) =

  9. Given  f(x) = x2 + 2x – 1, find  f(–3). • Step 1: re-write the equation. • Step 2: plug in your argument (-3) in for your unknown “x” • Step 3: Solve •   f(-3) = -32 + 2(-3) – 1 • Answer: f(-3) =

  10. Now you Try! • Given f(x) = x2 + 2x – 1. Evaluate f(–2)

  11. Evaluate the Function • F(x) = 2x -10 when f(x) = 6 • This is the opposite of the previous activity. • This equation states that your f(x) = 6 • So, in other words, the function of x equals 6. • You must now solve for “x”

  12. F(x) = 2x -10 when f(x) = 6 • 6 = 2x -10 Add 10 to both sides Divide by 2 X = 8

  13. Domain Vs. Range • A function consists of set called a domain and a set called the range. • A domain is a set that contains numbers called “inputs” • A range is a set of numbers called “outputs” • A pairing of inputs with outputs so that each input is paired with exactly one output An output may be paired with more than one input, but no input is paired with more than one output.

  14. Example What is the domain set ? What is the range set? How much would 20 gallons cost?

  15. Translating input and output to coordinate points Input (x) 0 3 1 5 4 Output(y) -1 1 5 7 9

  16. What would be the coordinate pairs?

  17. Write the Coordinate Pairs of the Function • F(3) = 4 • F(5) = 6 • F (7) = 8

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