Graph each function. ƒ(x) = log￬6 (x-2)

Question

Accepted Answer

After the following logarithmic function F of X equals log base eight X minus five. Now to graph this, we'll make use of some input and output values to plot onto our graph. Let's first make a table X and F of X. Now you notice we have an X minus five instead of our log function. This means we have a horizontal shift in particular or shifting to the right by five units. Now, by default, a log function has a domain from zero to infinity. In other words, the number inside the log function cannot be negative or zero. Let's say our first X value is five. We'll see what happens when we plug that in in a second. But we want values greater than five as well. Let's say we take 5.5, 678 and nine. Let's find what these output values are. Now, if we plugged in five, we would get F of five equals log base minus five. That is a slog base eight of zero. Now log of any base of zero is undefined because we cannot have a negative and separate log function. This value X equals five is an Asymptote. So I will draw, do a line here to indicate the ato that we have. Let's go ahead and plug in our other values, plugged in 5.5 wish to get negative 0.3 or three, five and six. We get a zero next 10.330 point 53 and finally, 0.67. Now we have five points, we can plot onto our graph. We have a point of 5.5 negative 0. 70.3380 point 53 and 90.67. We cannot make a smooth curve between all of these points. And because we have an a the left part of this function will go to negative infinity all the way down. So we can draw a line that looks kind of like this where we start from the bottom and left by the ascent to go up through our points and go flatten out to the rights. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function. ƒ(x) = log￬6 (x-2)

Key Concepts

Logarithmic Functions

Domain and Range

Graphing Techniques

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