Complete the table for the function y=10^x

Question

x y
–1
0
1
2

Now, graph the function.
Plot two points to graph the function.

Answer 1

To complete the table for the function \( y = 10^x \), we can calculate the values of \( y \) for each value of \( x \):

1. When \( x = -1 \): \[ y = 10^{-1} = \frac{1}{10} = 0.1 \]

2. When \( x = 0 \): \[ y = 10^{0} = 1 \]

3. When \( x = 1 \): \[ y = 10^{1} = 10 \]

4. When \( x = 2 \): \[ y = 10^{2} = 100 \]

Now, the completed table is as follows: \[ \begin{array}{|c|c|} \hline x & y \ \hline -1 & 0.1 \ 0 & 1 \ 1 & 10 \ 2 & 100 \ \hline \end{array} \]

Next, we will plot two points on the graph of the function \( y = 10^x \). We can choose two points from our table.

1. The point for \( x = 0 \) is \( (0, 1) \).
2. The point for \( x = 1 \) is \( (1, 10) \).

Graphing the Function:

• For the first point \( (0, 1) \): This is where the graph crosses the y-axis.
• For the second point \( (1, 10) \): This is where the graph shows significant growth.

Plotting the Points:

  y
  |
100|                          *
   |
 10|              *
   |
  1|      *
   |_____________________ x
   -1  0  1  2

In this representation, you can see the exponential growth of the function \( y = 10^x \) as \( x \) increases.