Question

question #5
consider the function $y = 2^{x}$. fill in the table below using your calculator and then sketch the graph on the grid provided. hint*** press y = 2 ^x on the graphing calculator

$x$

$y=2^{x}$

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$-3$

$-2$

$-1$

$0$

$1$

$2$

$3$

Explanation:

Step1: Calculate y for x=-3

$y=2^{-3}=\frac{1}{2^3}=\frac{1}{8}=0.125$

Step2: Calculate y for x=-2

$y=2^{-2}=\frac{1}{2^2}=\frac{1}{4}=0.25$

Step3: Calculate y for x=-1

$y=2^{-1}=\frac{1}{2^1}=\frac{1}{2}=0.5$

Step4: Calculate y for x=0

$y=2^{0}=1$

Step5: Calculate y for x=1

$y=2^{1}=2$

Step6: Calculate y for x=2

$y=2^{2}=4$

Step7: Calculate y for x=3

$y=2^{3}=8$

Answer:

Completed Table:

$x$	$y=2^x$
-2	$\frac{1}{4}$ or 0.25
-1	$\frac{1}{2}$ or 0.5
0	1
1	2
2	4
3	8

Graph Description:

Plot the points $(-3, 0.125)$, $(-2, 0.25)$, $(-1, 0.5)$, $(0, 1)$, $(1, 2)$, $(2, 4)$, $(3, 8)$ on the grid. Connect them with a smooth curve that approaches the x-axis (y=0) as $x$ approaches negative infinity, and increases rapidly as $x$ increases.