Consider the function: 𝑓(𝑥) = 3. 2

Let's go through each part of your request step by step.

### 7.1 Calculate the coordinates of the y-intercept of the graph of \( f \).

To find the y-intercept, we need to evaluate \( f(0) \):

\[
f(0) = 3 \cdot 2^0 - 6 = 3 \cdot 1 - 6 = 3 - 6 = -3
\]

The coordinates of the y-intercept are \( (0, -3) \).

### 7.2 Calculate the coordinates of the x-intercept of the graph of \( f \).

To find the x-intercept, we need to set the function equal to zero and solve for \( x \):

\[
3 \cdot 2^x - 6 = 0
\]

Solving for \( x \):

\[
3 \cdot 2^x = 6
\]
\[
2^x = 2
\]
\[
x = 1
\]

The coordinates of the x-intercept are \( (1, 0) \).

### 7.3 Sketch the graph of \( f \).

The function can be analyzed as follows:

1. **Y-intercept**: \( (0, -3) \)
2. **X-intercept**: \( (1, 0) \)
3. **Asymptote**: The function \( f(x) \) approaches \( -6 \) as \( x \) approaches negative infinity. Therefore, the horizontal asymptote is \( y = -6 \).

With these points and information, you can sketch the graph:
- Start by plotting the y-intercept at \( (0, -3) \) and the x-intercept at \( (1, 0) \).
- Plot the horizontal asymptote at \( y = -6 \).
- The function \( 3 \cdot 2^x \) is increasing and generally slopes upwards from left to right, crossing the y-axis at \( -3 \) and approaching \( -6 \) as \( x \) decreases.

### 7.4 Write down the range of \( f \).

Given the asymptote at \( y = -6 \) and considering that the function increases without bound as \( x \) increases, the range can be written as:

\[
\text{Range} = (-6, \infty)
\]

### Summary of Answers:
- **7.1** Y-intercept: \( (0, -3) \)
- **7.2** X-intercept: \( (1, 0) \)
- **7.3** Sketch includes y-intercept, x-intercept, and horizontal asymptote at \( y = -6 \) (drawing not possible in text).
- **7.4** Range of \( f \): \( (-6, \infty) \)