**How Will This Worksheet on "Domain and Range of Logarithmic Functions from Equation" Benefit Your Student's Learning?**

- Helps students grasp what logarithms are and how they work.
- Enhances skills in analyzing equations to determine permissible inputs (domain) and possible outputs (range).
- Makes it easier to solve real-world problems, like how things grow or shrink over time.
- Promotes critical thinking as students analyze how changes in the function's parameters affect its domain and range.
- Strengthens understanding of algebraic transformations affecting domain and range such as shifts and stretches.

**How to Domain and Range of Logarithmic Functions from an Equation?**

- Recognize the logarithmic function in the form \( y = \log_b(x) \), where \( b > 0 \) and \( b \neq 1 \).
- Logarithmic functions are defined for \( x > 0 \) because the logarithm of zero or a negative number is undefined in real numbers.
- The range of \( y = \log_b(x) \) includes all real numbers (\( y \in \mathbb{R} \)) because logarithmic functions can yield any real value depending on the input \( x \).
- Recognize how changes in the base \( b \) and any transformations affect the domain and range, such as shifts left or right on the `x`-axis and vertical stretches or compressions on the `y`-axis.