Here's an exponential function. y=((1)/(4))^x (a) Choose the graph that best represents the shape of this function. square

To determine the graph that best represents the shape of the exponential function \( y = \left(\frac{1}{4}\right)^x \), we need to understand the behavior of this function.1. **Base Analysis**: The base of the exponential function is , which is a fraction less than 1. This means the function is decreasing as increases.2. **Behavior for Positive and Negative **: - For : Since \(\left(\frac{1}{4}\right)^x\) is a fraction raised to a positive power, it gets smaller and smaller, approaching 0 but never reaching it. - For : \(\left(\frac{1}{4}\right)^x\) becomes \(\left(\frac{4}{1}\right)^{-x} = 4^x\), which grows exponentially as becomes more negative.3. **Asymptote**: The horizontal asymptote for this function is . As increases, approaches 0 from above.4. **Key Points**: - When : \( y = \left(\frac{1}{4}\right)^0 = 1 \) - When : \( y = \left(\frac{1}{4}\right)^1 = \frac{1}{4} \) - When : \( y = \left(\frac{1}{4}\right)^{-1} = 4 \)Given these characteristics, the graph of \( y = \left(\frac{1}{4}\right)^x \) will:- Start at \( (0, 1) \)- Decrease rapidly as increases- Approach the x-axis (y = 0) as increases- Increase rapidly as decreasesThe correct graph will show a curve that starts high on the left side (for negative ), passes through \( (0, 1) \), and then decreases towards the x-axis as increases.Without seeing the actual graphs, I can describe what the correct graph should look like:- It should be a smooth curve starting from the top left, passing through the point \( (0, 1) \), and then descending towards the x-axis as it moves to the right.If you have multiple-choice graphs to choose from, select the one that matches this description.