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Lesson_8.2_Transformations_of_Logarithmic_Functions

Lesson_8.2_Transformations_of_Logarithmic_Functions - (d...

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Lesson_8.2_Transformations_of_Logarithmic_Functions.notebook 8.2 Transformations of the Logarithmic Function Recall: The Logarithmic F n is the inverse of the Exponential F n For each exponential function, sketch the graph of the inverse and state its equation: x f(x) x g(x) = x f(x) x g(x)=

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Lesson_8.2_Transformations_of_Logarithmic_Functions.notebook Summary: the shape of the graph depends on the base value "a" if a>1 , we have increasing Exp. and Log. functions if a<1, we have decreasing Exp. and Log. functions Exponential Function Logarithmic Function Horizontal asymptote: Vertical asymptote: y­intercept: x­intercept: Domain: Domain: Range: Range: Recall: Transformations of Functions
Lesson_8.2_Transformations_of_Logarithmic_Functions.notebook For each of the following logarithmic functions, (a) Describe the transformations that must be applied to f( x ) = log 10 x to obtain g( x ). (b) Sketch the graph.

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Unformatted text preview: (d) If (100, 2) is a point on f(x), state the co-ordinates of its image point on g( x ). (i) g( x ) = 2log 10 ( x- 3) + 4 (ii) g( x ) = -log (2x + 2) - 5 Example 1: Example 2: Given the parent function f( x ) = log 10 x , state the equation of the function that results from each of the following transformations: (a) vertical compression by ¼, horizontal translation 5 units right, vertical translation 10 units up, reflection in the y-axis (b) reflection in the x-axis, vertical stretch by 5, horizontal shift 3 units left, vertical translation 12 units down Lesson_8.2_Transformations_of_Logarithmic_Functions.notebook Example 3: Without graphing, determine the domain of the function f( x ) = log 3 (9 -x 2 ). Homework Page 457 #1 – 3, 4(ii) (iii) (vi), 5abe, 9...
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