Answer:
AI-generated answer
To identify the range of the function y = 3 * ((1/2)ˣ) + 2, we need to determine the set of all possible values that the function can output or "reach".
Here are the steps to find the range:
1. Start by considering the base function f(x) = ((1/2)ˣ), which represents the exponential part of the given function.
2. The base function f(x) = ((1/2)ˣ) has a range that includes all positive values. As x approaches negative infinity, f(x) approaches 0, and as x approaches positive infinity, f(x) approaches infinity.
3. Next, multiply the base function f(x) by 3 to get 3 * ((1/2)ˣ). Multiplying a function by a positive constant doesn't change the range, so the range of 3 * ((1/2)ˣ) is also all positive values.
4. Finally, add 2 to the function 3 * ((1/2)ˣ). Adding a constant term doesn't change the shape or direction of the graph, it only shifts it vertically. So, the range of the function y = 3 * ((1/2)ˣ) + 2 is also all positive values, but shifted upward by 2 units.
In summary, the range of the function y = 3 * ((1/2)ˣ) + 2 is all positive values, including zero.
Step-by-step explanation: