Question

Use Desmos to graph the following exponential function then determine the domain and range.
y = 5 * (1.5) ^ w

Domain:
[ Select ]
all real numbers
x>0
x<0
Range:
[ Select ]
y<0
y>0
all real numbers

Answer 1

To analyze the exponential function \( y = 5 \cdot (1.5)^w \) using Desmos or similar graphing software, we can determine the domain and range as follows:

### Domain:
The domain of an exponential function is usually all real numbers because you can input any real number value for \( w \). Therefore:
- **Domain:** all real numbers

### Range:
For the range, since \( (1.5)^w \) is an exponential function that approaches 0 as \( w \) approaches negative infinity and grows without bound as \( w \) goes to positive infinity, we can multiply it by 5. Thus:
- The value of \( y \) will never be less than 0 (since any exponential function multiplied by a positive constant will still be non-negative).
- Therefore:
- **Range:** \( y > 0 \)

### Final Answers:
- Domain: **all real numbers**
- Range: **y > 0**