Question

graph the function ( y = 2^{x - 5}-1 ) using the given table of values and following the instructions below.

Explanation:

Step1: Plot the points

Take each pair \((x,y)\) from the tables and mark them on the coordinate plane. For example, when \(x = 4,y=-0.5\); when \(x = 5,y = 0\); when \(x=6,y = 1\) etc.

Step2: Connect the points

Since the function \(y=2^{x - 5}-1\) is an exponential function, connect the plotted points with a smooth curve. As \(x\to-\infty\), \(y = 2^{x-5}-1\approx - 1\) (horizontal asymptote \(y=-1\)). As \(x\) increases, the function grows exponentially.

Answer:

Plot the points from the tables \((x,y)\) (e.g., \((-10,-0.9999695),(-9,-0.999939),\cdots,(10,31)\)) on the coordinate plane and then connect them with a smooth curve that approaches the horizontal asymptote \(y = - 1\) as \(x\to-\infty\) and grows exponentially as \(x\) increases.