Understanding Functions: Examples and Non-Examples

What is a key characteristic of a function?

• Each output has exactly one input.

• Each input has exactly one output.

• Each input can have multiple outputs.

• Each output can have multiple inputs.

Which of the following is NOT a way to represent a function?

• Algebraically

• Verbally

• Numerically

• Graphically

In a mapping diagram, what indicates that a relation is a function?

• Each input is connected to multiple outputs.

• Each output is connected to multiple inputs.

• Each output is connected to exactly one input.

• Each input is connected to exactly one output.

Why is a relation with an input having multiple outputs not a function?

• Because it violates the rule of unique outputs for each input.

• Because it can be represented algebraically.

• Because it can be represented graphically.

• Because it allows multiple inputs for each output.

What is the result of using the input x = 5 in the function y = 4x - 3?

• 17

• 15

• 19

• 20

In the equation y = -2x^2 - 5x + 1, what happens when x = 2?

• The output is -1.

• The output is 17.

• The output is -17.

• The output is 0.

Why is the equation x^2 + y^2 = 16 not a function?

• Because it represents a parabola.

• Because it has a single output for each input.

• Because it has multiple outputs for some inputs.

• Because it represents a line.

What does the vertical line test determine?

• If a graph is a function.

• If a graph is a parabola.

• If a graph is a line.

• If a graph is a circle.

In the function y = 3^x, what is the output when x = 4?

• 64

• 16

• 81

• 27

What is the significance of the vertical line test in identifying functions?

• It shows if a graph is a line.

• It shows if a graph is a circle.

• It shows if a graph is a function by checking if any vertical line crosses the graph more than once.

• It shows if a graph is a parabola.