Answer:
Find the asymptotes.
Set the argument of the logarithm equal to zero.
x+5=0 . Subtract 5
from both sides of the equation. x=−5
The vertical asymptote occurs at x=−5
Vertical Asymptote: x=−5
Find the point at x=−4
Replace the variable x with −4
in the expression.
f(−4)=log((−4)+5)
Simplify the result. Add −4 and 5
f(−4)=log(1) Logarithm base 10 of 1 is 0
f(−4)=0
The final answer is 0
Convert 0 to decimal. y=0
Find the point at x=5. Replace the variable x with 5
in the expression.
f(5)=log((5)+5)
Simplify the result. Convert 1 to decimal. y=1
Find the point at x=−3
Replace the variable x with −3
in the expression.
f(−3)=log((−3)+5)
Simplify the result.
log(2) . Convert log(2) to decimal. y=0.30102999
The log function can be graphed using the vertical asymptote at x=−5 and the points (−4,0),(5,1),(−3,0.30102999)
Vertical Asymptote: x=−5
x y
−4 0
−3 0.301
5 1
Step-by-step explanation:
