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

To find the y-intercept of the function \( f(x) + 3 \), you need to evaluate the function when \( x = 0 \), as the y-intercept occurs when \( x = 0 \).

The given function is \( f(x) = 10x \), and the function we are analyzing is \( f(x) + 3 \). Let's calculate the y-intercept:

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

Thus, the coordinates of the y-intercept are \( (0, 3) \).

Would you like further clarification or more details?

Here are 5 related questions for you to explore:
1. How do you find the y-intercept for any linear function?
2. What is the slope of the function \( f(x) + 3 \)?
3. How do vertical shifts affect the y-intercept of a function?
4. Can you graph the function \( f(x) = 10x + 3 \) and identify the intercepts?
5. How would the y-intercept change if we added a different constant to \( f(x) \)?

**Tip:** The y-intercept represents the value of the function when \( x = 0 \). For any function, simply substitute \( x = 0 \) to find it.

Discover how to find the y-intercept of the function f(x) = 10x + 3. This tutorial explores linear functions, intercepts, and vertical shifts, providing a step-by-step solution. Ideal for students in Grades 6-8 learning about basic algebra.

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