Questions: Graph the function f(x)=2(1/2)^(x-5)-5 on the axes below. You must plot the asymptote and any two points with integer coordinates.

Transcript text: Graph the function $f(x)=2\left(\frac{1}{2}\right)^{x-5}-5$ on the axes below. You must plot the asymptote and any two points with integer coordinates.

Solution

Solution Steps

Step 1: Find the horizontal asymptote

The horizontal asymptote is given by the vertical shift, which is $y = -5$.

Step 2: Find two points with integer coordinates

We are looking for two points with integer coordinates. Let $x = 5$. Then $f(5) = 2(\frac{1}{2})^{5-5} - 5 = 2(\frac{1}{2})^0 - 5 = 2(1) - 5 = 2 - 5 = -3$. Thus, the point is $(5, -3)$.

Let $x = 6$. Then $f(6) = 2(\frac{1}{2})^{6-5} - 5 = 2(\frac{1}{2})^1 - 5 = 2(\frac{1}{2}) - 5 = 1 - 5 = -4$. Thus, the point is $(6, -4)$.