How do you graph #y=log (x-4)#?

Question

Kennedy Adams · Accepted Answer

Graph shows the vertical asymptote at x nearing 4.

X must be more than 4 otherwise log(x-4) will be invalid; Let us make a table of x & y #x rarr rarr log(x-4)# ------- ---------------- #5 rarr rarr 0# #9 rarr rarr .7# #14 rarr rarr 1# #19 rarr rarr 1.18# #24 rarr rarr 1.30# Now we can plot the Graph with the value of x and y.On this Graph Vertical asymptote is at x nearing the value 4. graph{log(x-4) [-20, 20, -10, 10]}

Julia Adams · Answer

undefined To graph $ y = \log(x - 4) $, follow these steps:

1. Determine the domain of the function. Since the argument of the logarithm must be positive, $ x - 4 > 0 $, so $ x > 4 $.

2. Identify any vertical asymptotes. Since the function is undefined for $ x = 4 $, there is a vertical asymptote at $ x = 4 $.

3. Find the x-intercept by setting $ y = 0 $ and solving for $ x $. $ 0 = \log(x - 4) $ implies $ x - 4 = 1 $, so $ x = 5 $.

4. Determine the behavior of the function as $ x $ approaches positive infinity. As $ x $ approaches positive infinity, $ \log(x - 4) $ approaches positive infinity.

5. Sketch the graph accordingly, considering the vertical asymptote at $ x = 4 $, the x-intercept at $ x = 5 $, and the behavior of the function as $ x $ approaches positive infinity.