Question

graphing exponentials and logarithms homework
graph the function ( f(x)=log _{2} x - 4 ) on the axes below. you must plot the asymptote and any two points with integer coordinates.
asymptote:

Explanation:

Step1: Find the vertical asymptote

For a logarithmic function \(y = \log_{a}x + k\), the vertical asymptote is \(x = 0\). So for \(f(x)=\log_{5}x - 4\), the vertical asymptote is \(x = 0\).

Step2: Find two points with integer coordinates

• Let \(x = 1\):

\(f(1)=\log_{5}1-4\). Since \(\log_{a}1 = 0\) for \(a>0,a
eq1\), then \(f(1)=0 - 4=-4\). So the point is \((1,-4)\).

• Let \(x = 5\):

\(f(5)=\log_{5}5-4\). Since \(\log_{a}a = 1\) for \(a>0,a
eq1\), then \(f(5)=1 - 4=-3\). So the point is \((5,-3)\).

Answer:

Asymptote: \(x = 0\); Two points: \((1,-4)\) and \((5,-3)\)