Question

graph the function ( y = 2^{x - 4}-5 ) using the given table of values and following the instructions below.
equation of asymptote:
( y=-5 )
plot at least four points from the table of values with integer coordinates on the axes below. click a point to delete it.

Explanation:

Step1: Identify integer - coordinate points

From the given tables, the points with integer coordinates are \((4,-4)\), \((5,-3)\), \((6,-1)\), \((7,3)\), \((8,11)\), \((9,27)\), \((10,59)\)

Step2: Plot the points

On the coordinate plane, for the point \((x = 4,y=-4)\), move 4 units to the right along the x - axis and 4 units down along the y - axis. For the point \((x = 5,y=-3)\), move 5 units to the right along the x - axis and 3 units down along the y - axis. For the point \((x = 6,y=-1)\), move 6 units to the right along the x - axis and 1 unit down along the y - axis. For the point \((x = 7,y = 3)\), move 7 units to the right along the x - axis and 3 units up along the y - axis.

Step3: Draw the asymptote

The equation of the horizontal asymptote is \(y=-5\). Draw a horizontal dashed line at \(y =-5\)

Step4: Sketch the curve

Connect the plotted points in a smooth curve that approaches the asymptote \(y=-5\) as \(x\to-\infty\)

Answer:

Plot the points \((4,-4)\), \((5,-3)\), \((6,-1)\), \((7,3)\) (or other valid integer - coordinate points from the tables) on the coordinate plane, draw the horizontal asymptote \(y =-5\) as a dashed line, and then sketch the exponential curve \(y=2^{x - 4}-5\) that passes through the plotted points and approaches the asymptote.