I need the number of solutions for f(x)=4

To determine the number of solutions for the equation \( f(x) = 4 \), we need to see where the graph of the function \( f(x) \) intersects the horizontal line \( y = 4 \).

### Analysis:
From the image, we can visually inspect the graph and identify how many times it intersects with the line \( y = 4 \).

1. Draw a horizontal line at \( y = 4 \) across the graph.
2. Count the number of intersection points between this line and the graph of \( f(x) \).

**From the graph**:
- The line \( y = 4 \) intersects the graph of \( f(x) \) at two distinct points. One intersection appears to be on the left side (negative \( x \)-axis), and the other on the right side (positive \( x \)-axis).

### Conclusion:
There are **2 solutions** for the equation \( f(x) = 4 \).

Would you like more details or further assistance with this problem?

### Related Questions:
1. How can we algebraically solve for \( x \) if the function \( f(x) \) is given explicitly?
2. What does the number of solutions represent in terms of the graph's behavior?
3. How would you determine the solutions if the graph intersects the line \( y = 4 \) more than twice?
4. How can you verify the solutions using a graphing calculator?
5. What would change if we were looking for \( f(x) = c \) for a different value of \( c \)?

### Tip:
When analyzing graphs for solutions to \( f(x) = c \), always draw the line \( y = c \) and count the intersection points to find the number of solutions.

Understand how to determine the number of solutions for the equation f(x) = 4 by analyzing its graph. Learn to draw a horizontal line at y = 4 and count the intersection points with the graph of f(x). This problem covers key mathematical concepts such as functions and graphing. Suitable for students in Grades 7-9.

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