complete the table for the function y = 5^x.\nnow, graph the function.\nplot two points to graph the function.

Explanation:

Step1: Recall the exponential - function formula

The function is $y = 5^{x}$.

Step2: Calculate $y$ for $x=-1$

Substitute $x = - 1$ into $y = 5^{x}$, we get $y=5^{-1}=\frac{1}{5}=0.2$.

Step3: Calculate $y$ for $x = 0$

Substitute $x = 0$ into $y = 5^{x}$, using the rule $a^{0}=1$ ($a\neq0$), so $y = 5^{0}=1$.

Step4: Calculate $y$ for $x = 1$

Substitute $x = 1$ into $y = 5^{x}$, then $y = 5^{1}=5$.

Step5: Calculate $y$ for $x = 2$

Substitute $x = 2$ into $y = 5^{x}$, we have $y = 5^{2}=25$.

To graph the function $y = 5^{x}$, we can use the points $(-1,0.2)$ and $(0,1)$ (or any other two points from the table). Plot these points on the coordinate - plane and draw a smooth curve passing through them. The curve will increase as $x$ increases and approach the $x$ - axis as $x\to-\infty$.

Answer:

The table is completed as shown in the problem statement. For graphing, two points such as $(-1,0.2)$ and $(0,1)$ can be plotted to draw the curve of $y = 5^{x}$.