Logarithmic functions LO Sketch logarithmic functions The graph

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Logarithmic functions LO: Sketch logarithmic functions.

Logarithmic functions LO: Sketch logarithmic functions.

The graph of y = 2 x You should be familiar with the graph

The graph of y = 2 x You should be familiar with the graph of y = 2 x -3 x y -2 6 -1 0 1 2 3 1 2 4 8 This is the graph of the exponential function y = 2 x. 5 4 3 The domain is the set of all real numbers. 2 1 0 -4 -3 -2 -1 0 -1 1 2 3 4 The range is the set of all positive real numbers. -2 -3 -4 -5 -6 Is asymptotic to the x-axis.

The graph of y = log 2 x If we switch the values of

The graph of y = log 2 x If we switch the values of x and y -3 x y -2 6 4 3 2 1 0 -3 -2 -1 0 -1 -2 0 1 2 3 1 2 4 8 This is the graph of the inverse function of y = 2 x. To get the inverse function f -1 of f(x) = 2 x y = 2 x 5 -4 -1 1 2 3 4 Switch x and y x = 2 y Take logs to the base 2 of both sides log 2 x = log 2 2 y log 2 x = y log 2 2 -3 -4 -5 -6 Since log 2 2 = 1 So f -1 = log 2 x = y

The graph of y = log 2 x If we switch the values of

The graph of y = log 2 x If we switch the values of x and y x y -3 6 5 -2 y = 2 x 4 y=x 3 2 1 0 -4 -3 -2 -1 0 -1 1 2 3 -2 -3 -4 -5 -6 y = log 2 x 4 -1 1 2 4 8 0 1 2 3 The graph of y = log 2 x is a reflection of y = 2 x in the line y = x As you can see, there is no part of the curve y = log 2 x in the second and third quadrants This is because, if x = 2 y, x is positive for al the real values of y

The logarithmic function y = loga x A logarithmic function, y = loga x,

The logarithmic function y = loga x A logarithmic function, y = loga x, has these properties: The domain is the set of all positive real numbers. The range is the set of all real numbers. The curve does not intercept the y-axis. The y-axis is a vertical asymptote y = loga x The x-intercept is 1 The graph is continually increasing

The graph of y = ln x Lets draw the graph of y =

The graph of y = ln x Lets draw the graph of y = ln x, x y -2 -1 1 e e 2 e 3 0 1 2 3 6 ⇒ 5 4 y = ln x 3 ⇒ 2 ⇒ 1 0 -12 -8 -4 0 -1 -2 -3 -4 -5 -6 4 8 12 16 20 ⇒ ⇒