Graphs of Logarithmic Functions

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Presentation transcript:

Graphs of Logarithmic Functions One more fun day in Section 3.3b

Let’s start with Analysis of the Natural Logarithmic Function: The graph: Domain: Range: Continuous on Increasing on No Symmetry Unbounded No Local Extrema No Horizontal Asymptotes Vertical Asymptote: End Behavior:

Note: Any other logarithmic function The “Do Now”  Analysis of the Natural Logarithmic Function The graph: Note: Any other logarithmic function with b > 1 has the same domain, range, continuity, inc. behavior, lack of symmetry, and other general behavior of the natural logarithmic function!!!

Reflect across the y-axis, Trans. right 3  The graph? Describe how to transform the graph of y = ln(x) or y = log(x) into the graph of the given function. Sketch the graph by hand and support your answer with a grapher. 1. Trans. left 2  The graph? 2. Reflect across the y-axis, Trans. right 3  The graph?

Vert. stretch by 3  The graph? Describe how to transform the graph of y = ln(x) or y = log(x) into the graph of the given function. Sketch the graph by hand and support your answer with a grapher. 3. Vert. stretch by 3  The graph? 4. Trans. up 1  The graph?

Trans. right 1, Horizon. shrink by 1/2, Describe how to transform the graph of y = ln(x) or y = log(x) into the graph of the given function. Sketch the graph by hand and support your answer with a grapher. 5. Trans. right 1, Horizon. shrink by 1/2, Reflect across both axes, Vert. stretch by 2, Trans. up 3  The graph???

1. Graph the given function, then analyze it for domain, range, continuity, increasing or decreasing behavior, boundedness, extrema, symmetry, asymptotes, and end behavior. 1. D: R: Continuous Dec: No Symmetry Unbounded No Local Extrema Asy: E.B.:

2. Graph the given function, then analyze it for domain, range, continuity, increasing or decreasing behavior, boundedness, extrema, symmetry, asymptotes, and end behavior. 2. D: R: Continuous Dec: No Symmetry Unbounded No Local Extrema Asy: E.B.: