The equation you provided is:

\[
y = \sqrt{7 - 5x}
\]

This is a square root function. Let's analyze it in detail:

### Domain:
The expression inside the square root, \(7 - 5x\), must be non-negative because the square root of a negative number is not a real number.

\[
7 - 5x \geq 0
\]

Solving for \(x\):

\[
7 \geq 5x
\]

\[
x \leq \frac{7}{5}
\]

So, the domain of \(y\) is \(x \leq \frac{7}{5}\).

### Range:
Since the square root function produces non-negative results, the range of \(y\) is \(y \geq 0\).

### Summary:
- **Domain:** \(x \leq \frac{7}{5}\)
- **Range:** \(y \geq 0\)

Would you like more details on any part of this analysis or have any other questions?

Here are some related questions to deepen your understanding:
1. How would you graph the function \(y = \sqrt{7 - 5x}\)?
2. What happens to the function if you change the coefficient of \(x\) from \(-5\) to \(-3\)?
3. How does the function behave as \(x\) approaches \(\frac{7}{5}\)?
4. What is the inverse function of \(y = \sqrt{7 - 5x}\)?
5. How would you solve \(y = \sqrt{7 - 5x}\) for \(x\)?

**Tip:** Always check the domain of a function involving square roots before solving or graphing to ensure you are working with real numbers.

Explore the square root function y = sqrt(7 - 5x) and its domain, range, and graphing. This mathematical problem delves into the concept of square root functions, suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation