Graph each function. ƒ(x) = log￬3 (x-1) + 2

Question

Accepted Answer

Graph. The following logic function F of X equals log base eight X minus six plus five. Now, to graph this, we'll find some input and output values to plot onto the graph. Let's make a table X and we have F of X. Now we notice here we have an X minus six inside of our log function. This means we have a shift, we shift our graph. So right then by six units now, because this is a log function, we cannot have the inside of our function equaling a negative number or zero. In other words, we have an ascent to at X equals six because we are shifted to the right by six. So for example, if I were to plug in six as a possible value, we should get an undefined. We'll check that in a second. Both also find some other values. We can say we have 6.5, 789 and 10. No, let's plug in our values. We plugged in six, we would get an un defect because we have log base 86 minus six plus five, which gives us life base eight of zero plus five. That is undefined. Let's say you plug in 6.5. Next, that will be 6.5 minus six plus five. If we were to plug this value in, we should get 4.67, be within get five. If you plugged in seven 5. 5 and eight, 5.53 opposed to nine 5.67. If we plugged in 10, now that we have all of our values, we can plot them onto our graph as mentioned before. We have an as at X equal six. So I will draw a dotted line here at X equal six for as now at 6.5, we go up to 4.67 seven, we go to five 85.33, 95.53 and 10 5.67. Like. So we can now make a smooth curve between all of our points. Since we have an Asymptote, this starts from negative infinity, goes up through our points and continues on up to infinity to the right. Ok. Well, this is how the graph of this function would look. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function. ƒ(x) = log￬3 (x-1) + 2

Key Concepts

Logarithmic Functions

Transformations of Functions

Domain and Range

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