Understanding Functions and Variables

Which of the following is the definition of a function?

• A relation where one input is paired with one output.

• A relation where one input is paired with multiple outputs.

• A relation that includes only numbers.

• A set of numbers that includes negative numbers.

In the relation {(2, 4), (3, 6), (4, 8), (2, 10)}, is it a function?

• Yes, because every input has a corresponding output.

• No, because input 2 is paired with two different outputs.

• Yes, because the outputs are different.

• No, because the inputs are the same.

Which of the following relations is not a function?

• {(1, 2), (2, 3), (3, 4)}

• {(5, 10), (5, 15), (6, 20)}

• {(-1, -2), (0, 0), (1, 2)}

• {(2, 3), (3, 6), (4, 8)}

Consider the relation {(x, y) | y = x^2}. Is this a function?

• Yes, because for each x, there is only one y.

• No, because x can have multiple values for y.

• Yes, because x is positive.

• No, because it’s not a linear relation.

A relation is defined as {(x, y) | x = 1}. Is this a function? Explain why.

• Yes, because there is only one y value for all x.

• No, because there are multiple y values for a single x.

• Yes, because all x values are the same.

• No, because the relation is constant.

The vertical line test helps determine if a relation is a function. Which of the following graphs represents a function?

• A straight line passing through all points.

• A circle.

• A parabola.

• A graph with vertical lines.

Which of the following real-life scenarios best represents a function?

• Assigning a student to a unique student ID number.

• Matching a person to their favorite foods.

• Mapping cities to their populations over time.

• Pairing students to multiple courses they are taking.

Given the set of ordered pairs {(1, 2), (3, 4), (5, 6)}, explain whether adding the pair (1, 7) would make the relation not a function.

• Yes, because 1 is already paired with 2.

• No, because 7 is a different number.

• Yes, because 7 is larger than 2.

• No, because each number is paired with exactly one.

What is the independent variable in an experiment?

• The variable you change.

• The variable that remains constant.

• The variable that depends on other factors.

• The variable you measure.

In an experiment measuring how the amount of sunlight affects plant growth, which is the dependent variable?

• The amount of sunlight.

• The height of the plants.

• The type of plant.

• The temperature of the room.