Explanation:
[tex]\begin{gathered} f(x)=log_4(x\text{ + 5)} \\ f(x)\text{ = }\frac{\log \text{ (x + 5)}}{\log \text{ 4}} \end{gathered}[/tex]
Let's assign values to x:
x = -5, -4, -3, -1, 1, 3
We replace value of x in the second function above to get f(x)
when x = -5
f(x) = infinity
when x = -4
f(x) = 0
x = -3
f(x) = 0.5
x = -1
f(x) = 1
x = 3
f(x) = 1.5
From the above, it shows x has to be greater than -5 to get value for f(x)
Domain of the function:
x > -5 since we can't get a result when x is -5 or less than that
[tex]\text{Domain: (-5, }\infty)[/tex]
Range: all real numbers
[tex]\text{Range: (-}\infty,\text{ }\infty)[/tex]
Plotting the graph:
End behaviour:
[tex]\begin{gathered} As\text{ x }\rightarrow\text{ }\infty,\text{ f(x) }\rightarrow\text{ }\infty \\ As\text{ x }\rightarrow-5^+,\text{ f(x) }\rightarrow\text{ -}\infty \\ -5^+\text{ means greater than -5} \end{gathered}[/tex][tex]undefined[/tex]
