Question

Graph the exponential function y equals 0.5(6) x squared identified y intercept

Answer 1

To graph the exponential function \( y = 0.5(6^x) \), you can follow these steps:

1. **Identify the Components**:
- This function has an exponential base of \( 6 \) and a multiplicative factor of \( 0.5 \).
- The function is defined for all real numbers \( x \).

2. **Determine the Y-Intercept**:
- The y-intercept occurs when \( x = 0 \):
\[
y = 0.5(6^0) = 0.5(1) = 0.5
\]
So the y-intercept is at the point \( (0, 0.5) \).

3. **Create a Table of Values**:
To help with plotting the graph, you can calculate some values:
\[
\begin{array}{|c|c|}
\hline
x & y = 0.5(6^x) \\
\hline
-2 & 0.5(6^{-2}) \approx 0.5 \cdot 0.0278 \approx 0.0139 \\
-1 & 0.5(6^{-1}) = 0.5 \cdot 0.1667 \approx 0.0833 \\
0 & 0.5(6^0) = 0.5 \\
1 & 0.5(6^1) = 0.5 \cdot 6 = 3 \\
2 & 0.5(6^2) = 0.5 \cdot 36 = 18 \\
\hline
\end{array}
\]

4. **Plot Points**:
The points from the table are:
- \( (-2, 0.0139) \)
- \( (-1, 0.0833) \)
- \( (0, 0.5) \)
- \( (1, 3) \)
- \( (2, 18) \)

5. **Graph the Function**:
- Plot the points on a graph.
- The curve will start near the x-axis as x becomes negative and rise steeply as x becomes positive.

6. **Draw the Curve**:
The graph will show a rapid increase as \( x \) increases because of the exponential nature of the function.

The general shape of the graph will be that of an exponential function starting from near zero (but never touching the x-axis) and increasing rapidly as \( x \) grows.

Remember, the curve approaches the x-axis (horizontal asymptote) as \( x \) approaches negative infinity but does not touch or cross it.

This graph illustrates the behavior of the function \( y = 0.5(6^x) \) with a clear identification of the y-intercept.