
If f(x)=10x, what are the coordinates for the y-intercept of f(x)+3?

Given the function \( f(x) = 10x \), we need to find the y-intercept of the function \( f(x) + 3 \).

1. **Expression for \( f(x) + 3 \):**
   \[
   f(x) + 3 = 10x + 3
   \]

2. **Y-intercept:** 
   The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation:
   \[
   y = 10(0) + 3 = 3
   \]

3. **Coordinates of the y-intercept:** 
   The y-intercept is at \( (0, 3) \).

So, the coordinates for the y-intercept of \( f(x) + 3 \) are \( \mathbf{(0, 3)} \).

Would you like further details or have any questions?

Here are some related questions you might find interesting:
1. What is the y-intercept of the original function \( f(x) = 10x \)?
2. How does shifting a graph vertically by a constant affect the y-intercept?
3. What are the x-intercepts of the function \( f(x) + 3 \)?
4. How would the graph of \( f(x) + 3 \) compare to the graph of \( f(x) \)?
5. What is the slope of the line \( f(x) + 3 = 10x + 3 \)?

**Tip:** The y-intercept of a function is found by setting \( x = 0 \) and solving for \( y \).

If f(x)=10x, what are the coordinates for the y-intercept of f(x)+3?

Discover how to find the y-intercept of the function f(x) + 3 where f(x) = 10x. This solution breaks down the steps to determine the coordinates of the y-intercept, covering key concepts like linear functions and graphing. Ideal for students in Grades 6-8.

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