Understand What are Exponential and Logarithmic Functions. click on the link to Watch the VIDEO explanation:Watch Video
Exponential and Logarithmic Functions
A general exponential function is of the form y is equal to f(x) is equal to b to the power of x with a positive base b greater than 1. Let us take a particular value for b as 2. To draw the graph of the function let us make a table of values. We take value of x between minus 2 and 2. Find a corresponding values of y. Key in the values.
We use this table to draw a graph of the function.
Let us now study the graph of the exponential function. y is equal to the b to the power of x for b is equal to 2. Domain of the exponential function is R, the set of real numbers. Range of the exponential function is R plus the set of all positive real numbers. The point (0,1) is always on the graph of the exponential function. An exponential function is always increasing when x is a very large negative number, y is a very small positive number. The negative x-axis is a horizontal asymptote of the curve.
A general logarithmic function is of the form y is equal to f(x) is equal to log x to the base b with a positive base b greater than 1. Let us take a particular value for b as 2. To draw the graph of the function we first make a table of values. We take values of x between 0.25 and 4. Find the corresponding values of y. Key in the values.
We use this table to draw the graph of the function.
Let us now study the graph of the logarithmic function. y is equal to the log x to the base b for b is equal to 2. Domain of the logarithmic function is R plus the set of all positive real numbers. Range of the logarithmic function is the set of real numbers. The point (1,0) is always on the graph of a logarithmic function. A logarithmic function is always increasing when x is between 0 and 1, the logarithm is negative. When x is very near to 0, y is a very small negative number. The negative y axis is a vertical asymptote of the curve.
For the exponential function f(x) is equal to b to the power of x. Its inverse function is the logarithmic function g(x) is equal to the log x to the base b. the graphs of f(x) and g(x) are reflection in the line y is equal to x.
Exponential and Logarithmic Functions
A general exponential function is of the form y is equal to f(x) is equal to b to the power of x with a positive base b greater than 1. Let us take a particular value for b as 2. To draw the graph of the function let us make a table of values. We take value of x between minus 2 and 2. Find a corresponding values of y. Key in the values.
We use this table to draw a graph of the function.
Let us now study the graph of the exponential function. y is equal to the b to the power of x for b is equal to 2. Domain of the exponential function is R, the set of real numbers. Range of the exponential function is R plus the set of all positive real numbers. The point (0,1) is always on the graph of the exponential function. An exponential function is always increasing when x is a very large negative number, y is a very small positive number. The negative x-axis is a horizontal asymptote of the curve.
A general logarithmic function is of the form y is equal to f(x) is equal to log x to the base b with a positive base b greater than 1. Let us take a particular value for b as 2. To draw the graph of the function we first make a table of values. We take values of x between 0.25 and 4. Find the corresponding values of y. Key in the values.
We use this table to draw the graph of the function.
Let us now study the graph of the logarithmic function. y is equal to the log x to the base b for b is equal to 2. Domain of the logarithmic function is R plus the set of all positive real numbers. Range of the logarithmic function is the set of real numbers. The point (1,0) is always on the graph of a logarithmic function. A logarithmic function is always increasing when x is between 0 and 1, the logarithm is negative. When x is very near to 0, y is a very small negative number. The negative y axis is a vertical asymptote of the curve.
For the exponential function f(x) is equal to b to the power of x. Its inverse function is the logarithmic function g(x) is equal to the log x to the base b. the graphs of f(x) and g(x) are reflection in the line y is equal to x.
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