graph the function ( y = 2^{x - 4}-5 ) using the given table of values and following the instructions…

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

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

Answer

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.