Question

complete the table for the function $y = 0.5^x$.

$x$	$y$
$-1$	\\(\square\\)
$0$	\\(\square\\)
$1$	\\(\square\\)

now, graph the function.
plot two points to graph the function.
(graph with x and y axes, grid lines, and labels)

Explanation:

Step1: Calculate y when x = -2

Substitute \( x = -2 \) into \( y = 0.5^x \), we get \( y = 0.5^{-2} = (\frac{1}{2})^{-2} = 2^2 = 4 \).

Step2: Calculate y when x = -1

Substitute \( x = -1 \) into \( y = 0.5^x \), we get \( y = 0.5^{-1} = (\frac{1}{2})^{-1} = 2^1 = 2 \).

Step3: Calculate y when x = 0

Substitute \( x = 0 \) into \( y = 0.5^x \), we get \( y = 0.5^0 = 1 \) (since any non - zero number to the power of 0 is 1).

Step4: Calculate y when x = 1

Substitute \( x = 1 \) into \( y = 0.5^x \), we get \( y = 0.5^1 = 0.5 \).

For graphing the function \( y = 0.5^x \) (which is an exponential function with base \( 0.5\lt1\), so it is a decreasing exponential function):

• We can use the points we calculated: \((-2,4)\), \((-1,2)\), \((0,1)\), \((1,0.5)\).
• Plot these points on the coordinate plane. For example, to plot \((-2,4)\), we move 2 units to the left of the origin on the x - axis and 4 units up on the y - axis. To plot \((-1,2)\), we move 1 unit to the left of the origin on the x - axis and 2 units up on the y - axis. To plot \((0,1)\), we are at the point (0,1) on the y - axis. To plot \((1,0.5)\), we move 1 unit to the right of the origin on the x - axis and 0.5 units up on the y - axis. Then we draw a smooth curve through these points.

Answer:

The completed table is:

x	y
-1	2
0	1
1	0.5

(For graphing, plot the points \((-2,4)\), \((-1,2)\), \((0,1)\), \((1,0.5)\) and draw a smooth curve through them.)