SOLUTION: Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its graph: y = log3(x-2) + 4
Please show me how you got the answers, thank you.
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Question 1130365: Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its graph: y = log3(x-2) + 4
Please show me how you got the answers, thank you.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
if you have this:
domain - The domain of is the set of all values such that
Solve the above inequality to obtain the domain:
{ element : }
The range of is given by the interval:
(, ).
b.
The vertical asymptote is obtained by solving the equation:
which gives
As approaches from the right () , decreases without bound because there is a vertical asymptote. How do we know this?
c.
- To find the - intercept we need to solve the equation or
Rewrite the above equation in exponential form:
The intercept is at the point
The intercept is at the point ( , )
=> ( , ) => have complex solution, there is no intercept
d - So far we have the domain, range, and intercepts and the vertical asymptote. We need more points to draw a graph.
table:
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plot points and draw a graph:
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