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Example Questions
Example Question #21 :How To Graph An Exponential Function
Give the-coordinate of the-intercept of the graph of the function
The-intercept of the graph ofis the point at which it intersects the-axis. Its-coordinate is 0; its-coordinate is, which can be found by substituting 0 forin the definition:
Example Question #22 :How To Graph An Exponential Function
Give the-coordinate of the-intercept of the graph of the function.
The graph ofhas no-intercept.
The-intercept of the graph ofis the point at which it intersects the-axis. Its-coordinate is 0; its-coordinate is, which can be found by substituting 0 forin the definition:
,
the correct choice.
Example Question #23 :How To Graph An Exponential Function
Give the-coordinate of the-intercept of the graph of the function.
The graph ofhas no-intercept.
The graph ofhas no-intercept.
The-intercept(s) of the graph ofare the point(s) at which it intersects the-axis. The-coordinate of each is 0,; their-coordinate(s) are those value(s) offor which, so set up, and solve for, the equation:
Subtract 7 from both sides:
Divide both sides by 2:
The next step would normally be to take the natural logarithm of both sides in order to eliminate the exponent. However, the negative numberdoes not have a natural logarithm. Therefore, this equation has no solution, and the graph ofhas no-intercept.
Example Question #24 :How To Graph An Exponential Function
Give the-coordinate of the-intercept of the graph of the function
The-intercept(s) of the graph ofare the point(s) at which it intersects the-axis. The-coordinate of each is 0,; their-coordinate(s) are those value(s) offor which, so set up, and solve for, the equation:
Add 8 to both sides:
Divide both sides by 2:
Take the common logarithm of both sides to eliminate the base:
Example Question #25 :How To Graph An Exponential Function
Give the domain of the function.
The set of all real numbers
The set of all real numbers
Let. This function is defined for any real number,所以的领域is the set of all real numbers. In terms of,
Sinceis defined for all real, so is; it follows thatis as well. The correct domain is the set of all real numbers.
Example Question #26 :How To Graph An Exponential Function
Give the range of the function.
The set of all real numbers
Since a positive number raised to any power is equal to a positive number,
Applying the properties of inequality, we see that
,
and the range ofis the set.