Question

match each equation with the sketch of its graph.

Explanation:

To solve this, we analyze each graph's key features (domain, range, starting point, direction) and match with the equation's properties. However, since the equations aren't provided, we assume common function types:

Graph 1 (Point (3, -2), x from 3 to 7, y ≥ -2):

Likely a function with domain \( x \geq 3 \), range \( y \geq -2 \) (e.g., square root shifted).

Graph 2 (Point (3, 2), x from 3 to 7, y ≥ 2):

Domain \( x \geq 3 \), range \( y \geq 2 \) (similar to shifted square root, positive y).

Graph 3 (Starts at (0,0), x ≥ 0, y decreasing):

Domain \( x \geq 0 \), range \( y \leq 0 \) (e.g., negative square root \( y = -\sqrt{x} \)).

Graph 4 (Starts at (0,0), x ≥ 0, y increasing):

Domain \( x \geq 0 \), range \( y \geq 0 \) (e.g., square root \( y = \sqrt{x} \) or exponential, but shape suggests square root).

For example, if equations include:

• \( y = \sqrt{x - 3} - 2 \): Matches Graph 1 (starts at (3, -2), increases).
• \( y = \sqrt{x - 3} + 2 \): Matches Graph 2 (starts at (3, 2), increases).
• \( y = -\sqrt{x} \): Matches Graph 3 (starts at (0,0), decreases).
• \( y = \sqrt{x} \) or \( y = 2^x - 1 \) (but shape is square root): Matches Graph 4 (starts at (0,0), increases).

To fully match, we need the equations, but the process is:

1. Identify the starting point (vertex) of each graph.
2. Check domain (x-values) and range (y-values).
3. Match with the equation’s domain, range, and transformation (shifts, reflections).

If the question is to match \( y = -\sqrt{x} \), it goes to Graph 3 (starts at (0,0), y decreases as x increases).
If matching \( y = \sqrt{x - 3} - 2 \), it goes to Graph 1 (starts at (3, -2)).

Final Answer (Example Matching):

• \( y = -\sqrt{x} \) → Graph 3
• \( y = \sqrt{x - 3} - 2 \) → Graph 1
• \( y = \sqrt{x - 3} + 2 \) → Graph 2
• \( y = \sqrt{x} \) → Graph 4

(Note: Adjust based on actual equations. The key is analyzing domain, range, and starting point.)

Answer:

To solve this, we analyze each graph's key features (domain, range, starting point, direction) and match with the equation's properties. However, since the equations aren't provided, we assume common function types:

Graph 1 (Point (3, -2), x from 3 to 7, y ≥ -2):

Likely a function with domain \( x \geq 3 \), range \( y \geq -2 \) (e.g., square root shifted).

Graph 2 (Point (3, 2), x from 3 to 7, y ≥ 2):

Domain \( x \geq 3 \), range \( y \geq 2 \) (similar to shifted square root, positive y).

Graph 3 (Starts at (0,0), x ≥ 0, y decreasing):

Domain \( x \geq 0 \), range \( y \leq 0 \) (e.g., negative square root \( y = -\sqrt{x} \)).

Graph 4 (Starts at (0,0), x ≥ 0, y increasing):

Domain \( x \geq 0 \), range \( y \geq 0 \) (e.g., square root \( y = \sqrt{x} \) or exponential, but shape suggests square root).

For example, if equations include:

• \( y = \sqrt{x - 3} - 2 \): Matches Graph 1 (starts at (3, -2), increases).
• \( y = \sqrt{x - 3} + 2 \): Matches Graph 2 (starts at (3, 2), increases).
• \( y = -\sqrt{x} \): Matches Graph 3 (starts at (0,0), decreases).
• \( y = \sqrt{x} \) or \( y = 2^x - 1 \) (but shape is square root): Matches Graph 4 (starts at (0,0), increases).

To fully match, we need the equations, but the process is:

1. Identify the starting point (vertex) of each graph.
2. Check domain (x-values) and range (y-values).
3. Match with the equation’s domain, range, and transformation (shifts, reflections).

If the question is to match \( y = -\sqrt{x} \), it goes to Graph 3 (starts at (0,0), y decreases as x increases).
If matching \( y = \sqrt{x - 3} - 2 \), it goes to Graph 1 (starts at (3, -2)).

Final Answer (Example Matching):

• \( y = -\sqrt{x} \) → Graph 3
• \( y = \sqrt{x - 3} - 2 \) → Graph 1
• \( y = \sqrt{x - 3} + 2 \) → Graph 2
• \( y = \sqrt{x} \) → Graph 4

(Note: Adjust based on actual equations. The key is analyzing domain, range, and starting point.)