functions and graphs

[bobby2345]

Sorry if this is the wrong sub-forum this question was given from my calculus class tho.

Let D(x) be the function that represents the distance from (1,1) to the point (x, f (x)) where f(x)= lnx. Find the rule for D(x) and the domain of the function D. Include a diagram (follow the guidelines for diagrams and graphs) that shows the graph of f, the point (1,1) and a line from that point to an arbitrary point (x, f (x)) on the graph of f. Explain how you determined the rule for D. Reference to the diagram will make this clear.

My thoughts:

• Finding domain from point (1,1) to (x,lnx)
• We need graph function D
• ​Finding x-coordinates etc

 

[Deleted member 4993]

Sorry if this is the wrong sub-forum this question was given from my calculus class tho.

Let D(x) be the function that represents the distance from (1,1) to the point (x, f (x)) where f(x)= lnx. Find the rule for D(x) and the domain of the function D. Include a diagram (follow the guidelines for diagrams and graphs) that shows the graph of f, the point (1,1) and a line from that point to an arbitrary point (x, f (x)) on the graph of f. Explain how you determined the rule for D. Reference to the diagram will make this clear.

My thoughts:

• Finding domain from point (1,1) to (x,lnx)
• We need graph function D
• ​Finding x-coordinates etc

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

Let D(x) be the function that represents the distance from (1,1) to the point (x, f (x)) where f(x)= lnx. Find the rule for D(x) and the domain of the function D.

This is just algebra, so you can use what you learned back then:

The "rule" part is asking you to find a formula for the distance between two points. This should suggest to you that you might find the Distance Formula (here) to be useful. What did you get when you plugged the two points into this Formula?

The "domain" part is asking you to figure out which x-values are allowable. For this, you'll need to take both the square root and the logarithm into account. What values are not allowed into each of these?

Include a diagram (follow the guidelines for diagrams and graphs) that shows the graph of f, the point (1,1) and a line from that point to an arbitrary point (x, f (x)) on the graph of f.

This also is just algebra: Graph the log function. (here) Plot the point. (here) Draw a line segment from the given point to some place on the graph of the given function. No specific line is required here; you can pick, as your other segment endpoint, whatever point on the log graph you like.

My thoughts:

• Finding domain from point (1,1) to (x,lnx)
• We need graph function D
• ​Finding x-coordinates etc

I'm sorry, but I don't know what you mean by this...?

Please reply with clarification. When you reply, please include a clear listing of your efforts so far. Thank you!