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

The y-intercept of a function occurs where \( x = 0 \).

Given the function \( f(x) = 10x \), the new function is \( f(x) + 3 = 10x + 3 \).

To find the y-intercept, substitute \( x = 0 \):

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

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

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What are the x-intercepts of \( f(x) + 3 \)?
2. How would the graph of \( f(x) = 10x \) shift if a constant other than 3 is added?
3. What are the coordinates of the y-intercept of \( f(x) = 10x - 5 \)?
4. How does the slope of a linear function affect its graph?
5. Can a function have more than one y-intercept?

**Tip:** A function can only have one y-intercept, but it may have multiple x-intercepts depending on its form.

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

Discover how to calculate the y-intercept for the linear function f(x) + 3, based on the equation f(x) = 10x. This detailed explanation covers fundamental algebraic concepts and is perfect for students in Grades 8-10.

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