Question

complete the paragraph.
the function ( y = log_2(x + 2) ) has a ( y )-intercept at and a vertical asymptote with the equation.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\).
Substitute \(x=0\) into \(y=\log_{2}(x + 2)\):
\(y=\log_{2}(0 + 2)=\log_{2}(2)\)
Since \(\log_{a}(a)=1\) (\(a>0,a
eq1\)), when \(a = 2\), \(y = 1\).

Step2: Find the vertical asymptote

For the function \(y=\log_{b}(u)\), the vertical asymptote occurs when \(u=0\).
For \(y=\log_{2}(x + 2)\), set \(u=x + 2\).
Solve \(x+2=0\), we get \(x=-2\).

Answer:

The function \(y = \log_{2}(x + 2)\) has a \(y\) - intercept at \(1\) and a vertical asymptote with the equation \(x=-2\).