Match the formulas with the graphs.

Matching Formulas and Graphs

Analysis:

• Graph A shows a straight line with a negative slope. This represents a linear function of the form y = mx + c where m is negative.
• Graph Б shows a curve that increases as x increases and is concave down. This is characteristic of a square root function, like y = \sqrt{x}.
• Graph B shows a hyperbola in the first and third quadrants, with branches approaching the x and y axes. This represents an inverse proportion function, of the form y = k/x where k is positive.

Formulas Provided:

1. y = \sqrt{2x}
2. y = \frac{2}{x}
3. y = 2 - \frac{x}{2}

Matching:

• Formula 1: y = \sqrt{2x} corresponds to Graph Б. This is a square root function, which has the shape shown in Graph Б.
• Formula 2: y = \frac{2}{x} corresponds to Graph B. This is an inverse proportion function, which results in a hyperbola shape as seen in Graph B.
• Formula 3: y = 2 - \frac{x}{2} can be rewritten as y = -\frac{1}{2}x + 2. This is a linear function with a negative slope (-1/2) and a y-intercept of 2. This matches Graph A.

Final Matches:

• Graph A corresponds to Formula 3
• Graph Б corresponds to Formula 1
• Graph B corresponds to Formula 2