Logarithmic function calculator f x intercept

Logarithmic function calculator f x intercept how to#

Finding the Domain of a Logarithmic FunctionД«efore working with graphs, we will take a look at the domain (the set of input values) for which the logarithmic function is defined. In this section we will discuss the values for which a logarithmic function is defined, and then turn our attention to graphing the family of logarithmic functions. For instance, what if we wanted to know how many years it would take for our initial investment to double? Figure 1 shows this point on the logarithmic graph. By graphing the model, we can see the output (year) for any input (account balance). Д«ut what if we wanted to know the year for any balance? We would need to create a corresponding new function by interchanging the input and the output thus we would need to create a logarithmic model for this situation. We already know that the balance in our account for any year t t can be found with the equation A = 2500 e 0.05 t. To illustrate, suppose we invest $ 2500 $ 2500 in an account that offers an annual interest rate of 5 %, 5 %, compounded continuously. In other words, logarithms give the cause for an effect. How do logarithmic graphs give us insight into situations? Because every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation. In Graphs of Exponential Functions, we saw how creating a graphical representation of an exponential model gives us another layer of insight for predicting future events.

Identify the domain of a logarithmic function.

That is, substitute the -value formula you found into and simplify it to arrive at the -value formula you found.

If you found formulas for parts (5) and (6), show that they work together.

( Hint: Consider inverse trigonometric functions.) The most helpful points from the table are.

The formula for the -values is a little harder.

Try to figure out the formula for the -values.

Complete the following table, adding a few choices of your own for and :.

Is there any relationship to what you found in part (2)? (Remember to express the -value as a multiple of, if possible.) Has it moved? Sketch the graph when and, and find the вЂ“ and -values for the maximum point.

Now consider other graphs of the form for various values of and.

It may be helpful to express the -value as a multiple of. Using a graphing calculator or other graphing device, estimate the вЂ“ and -values of the maximum point for the graph (the first such point where ). Representing the inverse function in this way is also helpful later when we graph a function and its inverse on the same axes. Since we typically use the variable to denote the independent variable and to denote the dependent variable, we often interchange the roles of and, and write. Consequently, this function is the inverse of, and we write. Doing so, we are able to write as a function of where the domain of this function is the range of and the range of this new function is the domain of. We can find that value by solving the equation for. Since is one-to-one, there is exactly one such value. Therefore, to find the inverse function of a one-to-one function, given any in the range of, we need to determine which in the domain of satisfies. The inverse function maps each element from the range of back to its corresponding element from the domain of.

Recall that a function maps elements in the domain of to elements in the range of.

Logarithmic function calculator f x intercept how to#

We can now consider one-to-one functions and show how to find their inverses.