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.

Responces:
A
B
C
D

Answer 1

To determine whether each relation is a function, we will check for the vertical line test (in the case of graphs) and the definition of a function (where each input corresponds to exactly one output).

Relation A:

• The pairs are: (4, 4), (5, 5), (5, 0), (7, 8), (10, 1).
• When x = 5, there are two different outputs (y = 5 and y = 0).
• Therefore, Relation A is not a function.

Relation B:

• This relation is described as a U-shaped curve with its vertex at (-4.2, 0).
• A vertical line drawn anywhere on the graph will intersect the curve at most once, indicating that for each x-value there is only one corresponding y-value.
• Therefore, Relation B is a function.

Relation C:

• The equation is \( y = 4x + 53 \).
• This is a linear equation, and for every x-value there is exactly one corresponding y-value.
• Therefore, Relation C is a function.

Relation D:

• The equation is \( y = 8x^2 \).
• This represents a parabola that opens upwards, and like the curve in Relation B, a vertical line will intersect the graph at most once for each x-value.
• Therefore, Relation D is a function.

Summary:

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

Responses:

• A → Not a function
• B → Function
• C → Function
• D → Function