Lesson 8 6 Topic To compare linear exponential

Differences and Ratios of Functions You can use patterns between consecutive data pairs to

State whether the table represents, linear, exponential or quadratic functions. Then write the function.

Determine the type of function and write the function. Common Ratio: . 5 Pick

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Lesson 8. 6 Topic: To compare linear, exponential and quadratic functions. EQ: What are the differences in linear, exponential and quadratic functions? Brainstorm all of the characteristics of each function. Linear: line, exponent of 1, constant changes in x and y, Exponential: exponent is variable, curved, pos or neg change but not both, grows the fastest over long periods of time, Quadratic: exponent of 2, U shaped, pos and neg change in same graph, symmetric,

Differences and Ratios of Functions You can use patterns between consecutive data pairs to determine which type of function models the data. The differences of consecutive y-values are called first differences. The differences of consecutive first differences are called second differences. Linear Function: The first differences are constant Exponential Function: Consecutive y-values have a common ratio. Quadratic Function: The second differences are constant In all cases, the differences of consecutive x-values need to be constant

State whether the table represents, linear, exponential or quadratic functions. Then write the function. First difference is constant. Linear Change in y is -3 y = -3 x + b pick point (0, 2) 2 = -3(0) + b 2=b Y = -3 x + 2 Consecutive y values have a common ratio. Exponential The second differences are constant. Quadratic X-intercepts are 4 and 8 y = a(x – 4)(x – 8) pick a point (2, 12) 12= a(2 – 4)(2 – 8) solve for a 12 = a(-2)(-6) 12 = 12 a y = 1(x – 4)(x – 8) a=1 Foil

Determine the type of function and write the function. Common Ratio: . 5 Pick a point Exponential 8 = a(1) a=8 (0, 8)