Question 4 Identify the key features for the function $$ y=\frac{1}{4}^{x} $$. Select all that apply The function decreases The function increases The $$ y $$-intercept is $$ \left(0, \frac{1}{4}\right) $$ $$ b1 $$ The $$ y $$-intercept is $$ (0,1) $$ $$ 0

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Question 4 Identify the key features for the function $$ y=\frac{1}{4}^{x} $$. Select all that apply The function decreases The function increases The $$ y $$-intercept is $$ \left(0, \frac{1}{4}\right) $$ $$ b>1 $$ The $$ y $$-intercept is $$ (0,1) $$ $$ 0

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For the function $$ y = \left(\frac{1}{4}\right)^x $$, let's analyze its key features:

1. **Behavior of the Function:**
   - **Base Analysis:** The base $$ b = \frac{1}{4} $$ is between 0 and 1 ($$ 0 < b < 1 $$).
   - **Implication:** For exponential functions of the form $$ y = b^x $$:
     - If $$ b > 1 $$, the function **increases** as $$ x $$ increases.
     - If $$ 0 < b < 1 $$, the function **decreases** as $$ x $$ increases.
   - Since $$ \frac{1}{4} $$ is less than 1, the function **decreases**.

2. **Y-Intercept:**
   - To find the y-intercept, set $$ x = 0 $$:
     $$
     y = \left(\frac{1}{4}\right)^0 = 1
     $$
   - Therefore, the y-intercept is $$ (0, 1) $$.

3. **Base Constraints:**
   - As established, $$ b = \frac{1}{4} $$ satisfies $$ 0 < b < 1 $$.

**Summary of Correct Features:**
- **The function decreases.**
- **The y-intercept is $$ (0, 1) $$.**
- **$$ 0 < b < 1 $$.**

### **Correct Options:**
- The function decreases
- The $$ y $$-intercept is $$ (0,1) $$
- $$ 0- The function decreases - The $$ y $$-intercept is $$ (0,1) $$ - $$ 0 < b < 1 $$

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