Chapter 8-2 Properties of Exponential Functions

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Presentation transcript:

Chapter 8-2 Properties of Exponential Functions Essential Question: How do the “h” and “k” in y = ex – h + k affect the graph of y = ex?

8-2: Properties of Exponential Functions The function y = bx is called the parent function. All exponential functions are called translations of the parent function. Translations can be reflections, stretches/shrinks or shifts.

8-2: Properties of Exponential Functions The factor “a” in y = abx can represent a stretch, shrink and/or reflection Stretches/Shrinks If a is a number greater than 1, it stretches the parent function vertically If a is a number less than 1, it shrinks the parent function vertically y = 4(2)x y = 2x y = ¼(2)x

8-2: Properties of Exponential Functions The factor “a” in y = abx can represent a stretch, shrink and/or reflection Reflection If a is a negative number, its graph is a vertical reflection y = 2x y = -1(2)x

8-2: Properties of Exponential Functions Shifts In the function y = abx-h + k: Just like we did back with translations of an absolute value graph h represents a horizontal shift (in the opposite direction) k represents a vertical shift (in the correct direction) y = (2)x+3 y = 2x y = (2)x - 6

8-2: Properties of Exponential Functions Identify the parent function of y = 8(½)x+2+3, then identify any translations Parent function: y = (½)x Translations: Vertical stretch by a factor of 8 Horizontal shift 2 units left Vertical shift 3 units up Your turn: 9(3)x-3-1 Parent function: Translations: y=(3)x Vertical stretch by a factor of 9 Horizontal shift 3 units right Vertical shift 1 unit down

8-2: Properties of Exponential Functions The number e Much like π, there is an irrational number e which gets used frequently when dealing with continuous growth. Your calculator has a key for ex Evaluate e2 to four decimal places Answer: 7.3891

8-1: Exploring Exponential Models Assignment Page 442 Problems 1 – 14, 18 – 23 (all problems) For problems 1 – 14: Don’t graph the problems. Instead, identify the parent function and any translations that occur (like we did earlier today)