Question

Graph this function.
y=3(4)^x
Plot two points to graph the function.

Answer 1

To graph the function \( y = 3(4)^x \), we can select two values for \( x \) and calculate the corresponding values of \( y \).

### Step 1: Choose values of \( x \)
Let's choose \( x = 0 \) and \( x = 1 \).

### Step 2: Calculate corresponding \( y \) values

**For \( x = 0 \):**
\[
y = 3(4)^0 = 3 \cdot 1 = 3
\]
So the point is \( (0, 3) \).

**For \( x = 1 \):**
\[
y = 3(4)^1 = 3 \cdot 4 = 12
\]
So the point is \( (1, 12) \).

### Step 3: Points collected
The two points we have are:
1. \( (0, 3) \)
2. \( (1, 12) \)

### Step 4: Graph the function
To graph this function, plot the points (0, 3) and (1, 12) on a coordinate plane. Connect the points with a smooth curve, keeping in mind that the function \( y = 3(4)^x \) is an exponential growth function that rises quickly as \( x \) increases.

### Additional points for reference (optional)
If you need additional points, you can calculate further, for example:

**For \( x = -1 \):**
\[
y = 3(4)^{-1} = 3 \cdot \frac{1}{4} = \frac{3}{4} \approx 0.75
\]
So the point is \( (-1, 0.75) \).

**For \( x = 2 \):**
\[
y = 3(4)^2 = 3 \cdot 16 = 48
\]
So the point is \( (2, 48) \).

Now you can graph these points to visualize the growth of the function. If you plot all these points, you'll see the steep rise of the exponential function.