Find g(x), where g(x) is the reflection across the x-axis of f(x)=7x–5.
Write your answer in the form mx+b, where m and b are integers.
g(x)=

To find the function \( g(x) \), which is the reflection of \( f(x) = 7x - 5 \) across the x-axis, we follow these steps:

1. **Reflection Across the X-axis**: Reflecting a function across the x-axis involves multiplying the function by \(-1\).

2. **Apply the Reflection**: Multiply the entire function \( f(x) = 7x - 5 \) by \(-1\).

\[
g(x) = -[7x - 5]
\]

3. **Simplify**:

\[
g(x) = -7x + 5
\]

Thus, the reflected function is \( g(x) = -7x + 5 \).

Do you want more details or have any questions? Here are five related questions:

1. What would \( g(x) \) be if \( f(x) = -7x + 5 \)?
2. How does reflecting \( f(x) = 7x - 5 \) across the y-axis differ from the x-axis reflection?
3. What is the effect on the graph of a linear function when it's reflected across the origin?
4. Can you find the x-intercept of the reflected function \( g(x) = -7x + 5 \)?
5. What happens if you reflect \( f(x) = 7x - 5 \) twice across the x-axis?

**Tip:** Reflecting a function across the x-axis inverts the sign of the output but keeps the input values the same.

Find g(x), where g(x) is the reflection across the x-axis of f(x)=7x–5. Write your answer in the form mx+b, where m and b are integers. g(x)=

Learn how to find the reflection of the linear function f(x) = 7x - 5 across the x-axis, expressed in the form mx+b. Understand the key algebraic concepts and the process of reflecting functions. Suitable for students in Grades 8-10.

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