# Domain And Range Of Exponential Functions From Equation Worksheet

## 6 problems

Understanding domain and range in exponential functions involves analyzing equations. For example, in $$y = a \cdot b^x$$ (where $$b > 0$$ and $$b \neq 1$$), the domain covers all real numbers, while the range depends on the sign of $$a$$. A worksheet on the domain and range of exponential functions helps practice these concepts and provides examples to illustrate applying domain and range restrictions in exponential functions.

Algebra 2
Exponential Functions

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

• Helps students understand how exponential functions work with different values.
• Teaches how to analyze equations to determine the domain and range.
• Knowing the domain and range aids in solving problems involving exponential functions.
• Enhances math skills by requiring thoughtful consideration of possible values and outcomes.
• Encourages students to think critically about mathematical rules and their applications.

## How to Domain and Range of Exponential Functions from an Equation?

1. Determine the base $$b$$ of the exponential function $$y = a \cdot b^x$$.

2. The domain includes all real numbers unless specified otherwise by restrictions (e.g., $$x \in \mathbb{R}$$).

3. For $$y = a \cdot b^x$$, the range depends on value of $$a$$:

• If $$a > 0$$, $$y > 0$$ (positive range).
• If $$a < 0$$, $$y < 0$$ (negative range).

## Solved Example

Q. What is the domain of this exponential function$?$$\newline$$y = \left(\frac{1}{8}\right)^{x+2}$
Solution:
1. Identify variable domain: Identify the variable representing the domain in $y = \left(\frac{1}{8}\right)^{x+2}$.$\newline$ Domain is the set of $x$ values.
2. Determine possible values: Determine the possible values of $x$ in $y = \left(\frac{1}{8}\right)^{x+2}$.$\newline$ For any value of $x$, $\left(\frac{1}{8}\right)^{x+2}$ is defined.$\newline$ Possible values of $x$: all real numbers.
3. Select domain of y: Select the domain of $y = \left(\frac{1}{8}\right)^{x+2}$.$\newline$ $x$ can be any real number.$\newline$ Domain: all real numbers.

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”