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

Write your response as an ordered pair. Do not include any spaces.

The y-intercept occurs when \( x = 0 \). To find the y-intercept of \( f(x) + 3 \), we first calculate:

\[
f(0) = 10^0 = 1
\]

Then, we add 3:

\[
f(0) + 3 = 1 + 3 = 4
\]

Thus, the coordinates of the y-intercept are \( (0, 4) \).

The ordered pair is:  
\( (0,4) \)

Would you like any additional details or have further questions?

Here are five related questions for further exploration:
1. What is the y-intercept of \( f(x) = 2^x + 3 \)?
2. What is the slope of \( f(x) = 10^x \) at \( x = 0 \)?
3. How does adding a constant to a function affect its graph?
4. How do you find x-intercepts of exponential functions?
5. What is the derivative of \( f(x) = 10^x \)?

**Tip:** The y-intercept of a function is found by evaluating the function at \( x = 0 \).

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

Learn how to find the y-intercept of the function f(x) = 10^x + 3. This problem covers concepts related to exponential functions and intercepts, providing a step-by-step explanation for high school students in Grades 9-12.

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