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

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

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

The y-intercept occurs when \( x = 0 \). So, substitute \( x = 0 \) into the equation to find the y-intercept:

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

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

Would you like further details or have any questions?

Here are 5 related questions:
1. What are the x-intercepts of \( f(x) + 3 \)?
2. How does the graph of \( f(x) + 3 \) differ from the graph of \( f(x) = 10x \)?
3. What is the slope of the line \( f(x) + 3 \)?
4. If you shift \( f(x) + 3 \) vertically by 2 units, what would the new equation be?
5. What are the y-intercepts of \( f(x) = 10x + c \) for various values of \( c \)?

**Tip**: The y-intercept is always found by setting \( x = 0 \) in the function equation.

Explore how to find the y-intercept for the linear function f(x) + 3 when f(x) = 10x. This problem involves key algebraic concepts such as linear functions and the y-intercept, suitable for students in Grades 7-9.

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