graphing exponentials and logarithms homework\ngraph the function ( f(x)=log _{2} x - 4 ) on the axes below…

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

Answer

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\neq1), 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\neq1), then (f(5)=1 - 4=-3). So the point is ((5,-3)).

Answer:

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