https://file.aiquickdraw.com/mathbot/file/1726231492412ojas7isj.jpg

The given function is \( f(x) = x^2 - 3 \), with a domain of \( 0 \leq x < 4 \). The question asks for the smallest value in the range of \( f(x) \).

### Step 1: Analyze the function
The function \( f(x) = x^2 - 3 \) is a quadratic function, opening upwards because the coefficient of \( x^2 \) is positive.

### Step 2: Find the minimum and maximum values of \( f(x) \)
For the given domain \( 0 \leq x < 4 \), we will evaluate \( f(x) \) at the endpoints:

- At \( x = 0 \):
  \[
  f(0) = 0^2 - 3 = -3
  \]
  
- At \( x = 4 \):
  \[
  f(4) = 4^2 - 3 = 16 - 3 = 13
  \]

### Step 3: Determine the range
Since the quadratic function is continuous and increasing for \( x > 0 \), the function will take all values between \( -3 \) (at \( x = 0 \)) and \( 13 \) (just before \( x = 4 \)).

### Conclusion:
The smallest value in the range of \( f(x) \) is \( -3 \). 

So, the correct answer is **C. -3**.

---

Do you have any further questions or want more details? Here are some related questions you might find useful:

1. What is the range of a quadratic function generally?
2. How do you determine the vertex of a quadratic function?
3. How can we find the minimum or maximum of a function without graphing?
4. What is the difference between the domain and the range of a function?
5. Can a quadratic function have a negative minimum value?

**Tip:** For quadratic functions, the vertex often plays a key role in determining the maximum or minimum values.

The domain for f(x) = x^2 - 3 is 0 ≤ x < 4. The smallest value in the range of f(x) is

Learn how to find the smallest value of the quadratic function f(x) = x^2 - 3 for the domain 0 ≤ x < 4. This solution covers key concepts like quadratic functions, domain, range, and evaluating functions at critical points. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation