Question
Graph this function.
y=3(6)^x
Plot two points to graph the function.
y=3(6)^x
Plot two points to graph the function.
Answers
GPT-4o mini
To graph the function \( y = 3(6)^x \), let's identify two points by plugging in different values for \( x \).
1. **Choose \( x = 0 \)**:
\[
y = 3(6)^0 = 3(1) = 3
\]
So the first point is \( (0, 3) \).
2. **Choose \( x = 1 \)**:
\[
y = 3(6)^1 = 3(6) = 18
\]
So the second point is \( (1, 18) \).
Now we have two points:
- \( (0, 3) \)
- \( (1, 18) \)
### Graphing
To sketch the graph of the function \( y = 3(6)^x \):
- Plot the point \( (0, 3) \) on the graph.
- Plot the point \( (1, 18) \) on the graph.
The function is an exponential growth function, meaning it will increase rapidly as \( x \) increases.
### Summary of Points:
- \( (0, 3) \)
- \( (1, 18) \)
### Basic Shape:
The graph will start at the point \( (0, 3) \) and increase steeply as \( x \) increases. As \( x \) approaches negative infinity, \( y \) will approach 0 but never actually reach it (the horizontal asymptote at \( y = 0 \)).
1. **Choose \( x = 0 \)**:
\[
y = 3(6)^0 = 3(1) = 3
\]
So the first point is \( (0, 3) \).
2. **Choose \( x = 1 \)**:
\[
y = 3(6)^1 = 3(6) = 18
\]
So the second point is \( (1, 18) \).
Now we have two points:
- \( (0, 3) \)
- \( (1, 18) \)
### Graphing
To sketch the graph of the function \( y = 3(6)^x \):
- Plot the point \( (0, 3) \) on the graph.
- Plot the point \( (1, 18) \) on the graph.
The function is an exponential growth function, meaning it will increase rapidly as \( x \) increases.
### Summary of Points:
- \( (0, 3) \)
- \( (1, 18) \)
### Basic Shape:
The graph will start at the point \( (0, 3) \) and increase steeply as \( x \) increases. As \( x \) approaches negative infinity, \( y \) will approach 0 but never actually reach it (the horizontal asymptote at \( y = 0 \)).