f(x)=log13(x+5)
The vertical asymptote is found by setting x+5 equal to zero.
x+5=0⇒x=−5
The base of the log is 13. A base that is less than one indicates that the graph is a decreasing log.
To find the x intercept, set f(x)=0
0=log13(x+5)
Rewrite as an exponential and solve.
(13)0=x+5
1=x+5
x=−4 when f(x)=0⇒ the x intercept is (−4,0)
The y intercept is found by setting x=0
y=log13(0+5)
y=log135
Use the change of base formula logab=logbloga
y=log5log(13)=−1.46⇒the y intercept is (0,−1.46)
See the graph below.
useruploads.socratic.org)
Alternatively, the function can be rewritten as an exponential and an xy table can be constructed by choosing values of y and finding corresponding x values.
y=log13(x+5)
x+5=(13)y
x=(13)y−5
Then choose values of y such as −2,−1,0,1,2 and find the corresponding values of x. Plot the resulting xy coordinates.
