Section 5.1 The Natural Logarithmic Function: Differentiation.

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Presentation transcript:

Section 5.1 The Natural Logarithmic Function: Differentiation

For n = x If x > 1, ln x > x If 0 < x < 1, ln x < 0

Properties of the Natural Logarithmic Function 1.The domain is (0, ∞) and the range is (-∞, ∞). 2.The function is continuous, increasing, and one-to-one (monotonically increasing). 3.The graph is concave down. 1 1

Transformations of y = ln x 1. Vertical shift – up a units 1 1 2

Transformations of y = ln x 2. Horizontal shift – right a units 1 1

Transformations of y = ln x sarah ritter 3. Reflection about the x-axis 1 1

Transformations of y = ln x 4. Reflection about the y-axis

Transformations of y = ln x 5. Stretches graph vertically 1 1 2

Transformations of y = ln x 6. Stretches graph horizontally 1 1 2