What happens to the graph when “a” is a positive number? Show this with a sketch f(x) = ¼ (2) x and f(x) = 4 (2)^x

The graph above illustrates the two exponential functions:

1. **\( f(x) = \frac{1}{4} \cdot 2^x \)** (blue curve) - The graph grows slowly as \( x \) increases, starting at \( \frac{1}{4} \) when \( x = 0 \). It is compressed vertically.
2. **\( f(x) = 4 \cdot 2^x \)** (green curve) - This graph grows rapidly, starting at \( 4 \) when \( x = 0 \). It is stretched vertically, making the increase in \( f(x) \) faster.

When "a" is a positive number:
- If \( a \) is less than 1, the graph grows more slowly and is compressed.
- If \( a \) is greater than 1, the graph grows more rapidly and is stretched.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the graph change if \( a \) were negative?
2. What happens to the graph as \( a \) approaches zero?
3. How does changing the base (from 2 to another value) affect the shape of the graph?
4. How does the y-intercept change with different values of \( a \)?
5. What is the effect of shifting the graph horizontally?

**Tip:** In exponential functions, changing the base affects the rate of growth, but changing \( a \) only affects the vertical stretch or compression.

What happens to the graph when 'a' is a positive number? Show this with a sketch f(x) = ¼ (2)^x and f(x) = 4 (2)^x

Explore how positive values of 'a' affect the graphs of exponential functions f(x) = ¼(2)^x and f(x) = 4(2)^x. Understand vertical stretching and compression through detailed analysis. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation