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

The function given is \( f(x) = 10x \), and you're asked to find the y-intercept of \( f(x) + 3 \).

The y-intercept occurs where \( x = 0 \). So, to find the y-intercept, substitute \( x = 0 \) into the equation \( f(x) + 3 \).

\[
f(x) + 3 = 10x + 3
\]

When \( x = 0 \):

\[
f(0) + 3 = 10(0) + 3 = 0 + 3 = 3
\]

Therefore, the y-intercept is at \( (0, 3) \).

### Do you need more details or have any questions?

Here are some related questions for further exploration:
1. What is the slope of the line represented by \( f(x) + 3 \)?
2. How would the graph of \( f(x) + 3 \) differ from the graph of \( f(x) \)?
3. What are the coordinates of the x-intercept of \( f(x) + 3 \)?
4. How does shifting the function vertically affect its intercepts?
5. What is the domain and range of \( f(x) + 3 \)?

**Tip**: Always check the impact of constants added or subtracted on the y-intercept, as it represents a vertical shift.

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

Learn how to find the y-intercept of the linear function f(x) = 10x + 3. This step-by-step guide covers key concepts such as linear functions, y-intercepts, and vertical shifts. Suitable for students in Grades 6-8.

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