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Today’s Lesson: Comparing Linear, Quadratic, & Exponential Functions
December,14, 2017
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Linear Function Basic Algebraic Form:
Slope-intercept form is y = mx + b
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Linear Functions y = 3x + 5 X -1 1 2 Y 5 8 11 When the function is linear then there is a constant difference between each of the y values & x-values (SAME SLOPE!)
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Word Problem - Linear ABC bowling charges $5 for shoe rental and then an additional $3 per game bowled. If Chelsie bowls 4 games, how much will she have to pay?
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Exponential Function Basic Algebraic Form:
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Exponential Functions
Y =0.5(2)x X -1 1 2 Y 0.25 0.5 If you notice the differences are not the same, then try dividing the y values to find a common ratio.
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Word Problem – Exponential
A colony of bacteria has a mass grams and doubles every hour. How much will the colony of bacteria weigh after 6 hours?
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Quadratic Functions
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Quadratic Functions Y = x2 – 2x + 0 X -1 1 2 3 Y
1 2 3 Y If the differences are not the same. (3 - 0 = 3, and = 1) And the ratios are not the same ( 0/3 = 0 and -1/0 = undefined). Then this function is neither linear nor exponential. *But if the second differences are the same then the function is quadratic.
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Word Problem – Quadratic
The product of a number and the number minus four is -3. What is the number?
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Identifying from an equation:
Linear Has an x with no exponent. y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic Has an x2 in the equation. y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7 Exponential Has an x as the exponent. y = 3x + 1 y = 52x 4x + y = 13
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Examples: LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2
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Using differences and ratios to tell whether the values in the table represent a linear, exponential or quadratic function. X 1 2 3 4 Y -1 -2 -3 X -2 -1 1 2 Y -4 X -1 1 2 3 Y 16 4 1/16 X -3 -2 -1 1 Y 13.5 6 1.5
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A chambered nautilus is a marine animal that lives in the outermost chamber of its shell. When the Nautilus outgrows a chamber it adds a new, larger chamber to its shell. The table shows the volumes (in cubic cm) of consecutive chambers of a nautilus. Tell whether the data can be modeled by a linear function, an exponential function, or a quadratic function. Chamber 1 2 3 4 5 6 Volume (cm3) 0.837 0.889 0.945 1.005 1.068 1.135
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The table shows the body temperature B (in degrees Celsius) of a desert spiny lizard at various air temperatures A (in degrees Celsius) Tell whether the data can be modeled by a linear function, an exponential function, or a quadratic function. Air Temp, A (ºC) 26 27 28 29 30 Body Tem (ºC) 33.44 33.78 34.12 34.46 34.80
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The time it takes for a clock’s pendulum to swing from one side to another and back again is called the pendulums period. The table shows the period t (in seconds) of a pendulum of length l (in feet). Tell whether the data can be modeled by a liner function, and exponential function or a quadratic function. Period, t(sec) 1 2 3 4 5 Length, l (ft) 0.82 3.28 7.38 13.12 20.5
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Is the table linear, quadratic or exponential?
y 1 2 -1 3 4 5 8 x y 1 3 2 9 27 4 81 5 243 x y 1 5 2 9 3 13 4 17 21
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Comparing Functions Worksheet
Homework Comparing Functions Worksheet
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