Question

Find the domain and range of f(x)=14x+11 . Write the domain and range in interval form, using inequalities, and in set notation.(4 points)

Answer 1

To find the domain and range of the function \( f(x) = 14x + 11 \):

### Domain:
The domain of a function is the set of all possible input values (x-values). Since \( f(x) = 14x + 11 \) is a linear function, there are no restrictions on the values of \( x \). Therefore, the domain is all real numbers.

- **Interval Form:** \( (-\infty, \infty) \)
- **Inequalities:** \( x \in (-\infty, \infty) \)
- **Set Notation:** \( \{ x \, | \, x \in \mathbb{R} \} \)

### Range:
The range of a function is the set of all possible output values (y-values). For the linear function \( f(x) = 14x + 11 \), as \( x \) takes on all real values, \( f(x) \) will also take on all real values because the slope is non-zero.

- **Interval Form:** \( (-\infty, \infty) \)
- **Inequalities:** \( f(x) \in (-\infty, \infty) \)
- **Set Notation:** \( \{ f(x) \, | \, f(x) \in \mathbb{R} \} \)

### Summary:
- **Domain:**
- Interval Form: \( (-\infty, \infty) \)
- Inequalities: \( x \in (-\infty, \infty) \)
- Set Notation: \( \{ x \, | \, x \in \mathbb{R} \} \)

- **Range:**
- Interval Form: \( (-\infty, \infty) \)
- Inequalities: \( f(x) \in (-\infty, \infty) \)
- Set Notation: \( \{ f(x) \, | \, f(x) \in \mathbb{R} \} \)