### About Domain and Range:

When working with relations and functions, we will sometimes be asked to find the domain and range of a relation or function from its equation or its graph. If we want to find the domain, we will inspect our equation and ask the question: what is allowed as a replacement for our independent variable x? For the range, we will think about the possible outputs or y-values, given the possible x-values.

Test Objectives

- Demonstrate the ability to find the domain and range of a relation or function from a graph
- Demonstrate the ability to find the domain of a relation or function

#1:

Instructions: find the domain and range.

$$a)\hspace{.2em}y=-3x - 2$$

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#2:

Instructions: find the domain and range.

$$a)\hspace{.2em}y=\sqrt{x + 1}- 3$$

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#3:

Instructions: find the domain.

$$a)\hspace{.2em}y=-\frac{7}{x^2 - 4x - 5}$$

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#4:

Instructions: find the domain.

$$a)\hspace{.2em}y=\frac{\sqrt{3x - 2}}{6x^2 + 8x - 30}$$

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#5:

Instructions: find the domain.

$$a)\hspace{.2em}y=\frac{\sqrt{35x^2 - 58x - 9}}{\sqrt{x^2 - 2x + 1}}$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}Domain: \{x|x \in \mathbb{R}\}$$ $$Range: \{y|y \in \mathbb{R}\}$$

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#2:

Solutions:

$$a)\hspace{.2em}Domain: \{x|x≥ -1\}$$ $$Range: \{y|y ≥ -3\}$$

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#3:

Solutions:

$$a)\hspace{.2em}Domain: \{x | x ≠ -1, 5\}$$

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#4:

Solutions:

$$a)\hspace{.2em}Domain: \left\{x | x ≥ \frac{2}{3}, x ≠ \frac{5}{3}\right\}$$

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#5:

Solutions:

$$a)\hspace{.2em}Domain: \left\{x | x ≤ -\frac{1}{7}, x ≥ \frac{9}{5}\right\}$$