Question

Graph.fill in blanks. And fill in the table. (For the points selected)

Answer 1

Explanation:

$\begin{gathered} f(x)=log_4(x\text{ + 5)} \\ f(x)\text{ = }\frac{\log \text{ (x + 5)}}{\log \text{ 4}} \end{gathered}$

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

$\text{Domain: (-5, }\infty)$

Range: all real numbers

$\text{Range: (-}\infty,\text{ }\infty)$

Plotting the graph:

End behaviour:

$\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}$$undefined$