https://file.aiquickdraw.com/mathbot/file/1728916395360qodwi8e1.jpg

The question is asking which point lies on the graph of the function \( f(x) = 4^x \).

To determine which point is on the graph, let's check the values of \( f(x) = 4^x \) for the \( x \)-values in the given options:

1. **Option A: (0, 0)**
   \[
   f(0) = 4^0 = 1 \quad \text{(not equal to 0)}
   \]
   So, \( (0, 0) \) is **not** on the graph.

2. **Option B: (0, 4)**
   \[
   f(0) = 4^0 = 1 \quad \text{(not equal to 4)}
   \]
   So, \( (0, 4) \) is **not** on the graph.

3. **Option C: (1, 4)**
   \[
   f(1) = 4^1 = 4
   \]
   This matches the point \( (1, 4) \). So, this point is **on the graph**.

4. **Option D: (4, 1)**
   \[
   f(4) = 4^4 = 256 \quad \text{(not equal to 1)}
   \]
   So, \( (4, 1) \) is **not** on the graph.

The correct answer is **Option C: (1, 4)**.

Would you like any further explanation or details on this?

### 5 Related Questions:
1. How do you graph exponential functions like \( f(x) = 4^x \)?
2. What are the key characteristics of an exponential growth function?
3. How can we determine the domain and range of \( f(x) = 4^x \)?
4. How does changing the base in an exponential function affect its graph?
5. How can we solve for \( x \) in equations of the form \( 4^x = y \)?

### Tip:
In exponential functions of the form \( f(x) = a^x \), as \( x \) increases, the function grows rapidly for \( a > 1 \), and the graph has a horizontal asymptote at \( y = 0 \).

Which point is on the graph of f(x) = 4^x?

This problem involves identifying the correct point on the graph of an exponential function, f(x) = 4^x. Explore exponential functions, key concepts, and how to evaluate points using f(x) = a^x. This is suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation