Four relations are shown.

Question

Relation A has two columns x and y. When x is 4, y is 4. When x is 5, y is 5. When x is 5, y is 0. When x is 7, y is 8. When x is 10, y is 1. Relation B has a coordinate plane with a U-shaped curve open to the right with its vertex at (-4.2, 0). Relation C shows the equation 4x plus 53 equals to y. Relation D shows the equation y equal to 8x exponential 2.

Drag the name of each relation to identify whether the relation is a function or not a function.
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Answer 1

Let's analyze each relation to determine if they are functions:

1. Relation A: This relation has two columns (x, y). To be a function, each input (x) must map to exactly one output (y).

   • When x is 4, y is 4 → valid
   • When x is 5, there are two outputs (y = 5 and y = 0) → not valid
   • When x is 7, y is 8 → valid
   • When x is 10, y is 1 → valid Since there are multiple outputs (y values) for the same input (x = 5), Relation A is not a function.

2. Relation B: This relation shows a U-shaped curve (which means it could represent a quadratic function) open to the right with its vertex at (-4.2, 0).

   • This relation can be expressed in the form of a function, where any x-value has a unique corresponding y-value. Therefore, Relation B is a function.

3. Relation C: The equation given is \( 4x + 53 = y \), which can be rearranged to \( y = 4x + 53\).

   • This is a linear equation and each input (x) will map to exactly one output (y). Therefore, Relation C is a function.

4. Relation D: The equation given is \( y = 8x^2 \), which describes a quadratic function.

   • Similar to Relation B, for each x-value, there is a unique y-value, meaning it satisfies the definition of a function. Thus, Relation D is also a function.

In summary:

• Relation A: Not a function
• Relation B: Function
• Relation C: Function
• Relation D: Function