Answer:
The function f(x) = ln(x - 4) is graphed the question options
Explanation:
* Lets study the the information of the problem
- The graph of a logarithmic has a vertical asymptote at x=4
* That means the curve gets closer and closer to the vertical line x = 4
but does not cross it
- It contains the point (e+4, 1)
* That means if we substitute x = e + 4 in the equation the value
of y will be equal to 1
- It has an x-intercept of 5
* That means if we substitute y = 0 in the equation the value of x
will be equal to 5
* Lets find the right answer
∵ f(x) = ln(x - 4)
* To find the equation of the asymptote let x - 4 = 0
∵ x - 4 = 0
∴ x = 4
∴ f(x) has a vertical asymptote at x = 4
* Lets check the point (e + 4 , 1) lies on the graph of the f(x)
∵ x = e + 4
∴ f(e+4) = ln(e + 4 - 4) = ln(e)
∵ ln(e) = 1
∴ The point (e+4 , 1) lies on the graph of the function f(x)
* To find the x-intercept put y = 0
∵ f(x) = 0
∴ ln(x - 4) = 0
* Change the logarithmic function to the exponential function
- The base of the ln is e
∴ e^0 = x - 4
∵ e^0 = 1
∴ x - 4 = 1 ⇒ add 4 to the both sides
∴ x = 5
* The function f(x) = ln(x - 4) is graphed the question options