Question

Graph this function.
y=5(4)^x
Plot two points to graph the function.

Answer 1

To graph the function \( y = 5(4)^x \), we can choose a couple of values for \( x \) to find corresponding \( y \) values. Let's choose \( x = 0 \) and \( x = 1 \).

### Calculating Points:

1. **For \( x = 0 \):**
\[
y = 5(4)^0 = 5(1) = 5
\]
So, the first point is \( (0, 5) \).

2. **For \( x = 1 \):**
\[
y = 5(4)^1 = 5(4) = 20
\]
So, the second point is \( (1, 20) \).

### Points to Plot:
- \( (0, 5) \)
- \( (1, 20) \)

### Graphing:

To create the graph:

- Plot the point \( (0, 5) \) on the coordinate plane, which is on the y-axis.
- Plot the point \( (1, 20) \), which is one unit to the right and twenty units up from the origin.

### Characteristics of the Function:
- The function is an exponential function that increases rapidly as \( x \) increases.
- As \( x \) approaches negative values, \( y \) approaches 0 but never actually reaches it.

You can sketch the curve starting from near the x-axis for negative \( x \), passing through the points you plotted, and increasing sharply as \( x \) becomes larger.