Exploring Functions and Relations through the Vertical Line Test

What is the main difference between a function and a relation?

• A relation is always a function.

• A function has only one output for each input.

• A relation can have only one output for each input.

• A function can have multiple outputs for a single input.

What does the notation f(x) represent?

• The function itself.

• The output of a function.

• The input of a function.

• The variable y in an equation.

If f(x) = 3x + 1, what is f(2)?

• 5

• 9

• 7

• 8

Why is function notation useful?

• It makes equations easier to solve.

• It is required for all mathematical equations.

• It provides more information at a glance.

• It simplifies the graphing process.

How can you tell if an equation is a function?

• By graphing the equation.

• By checking if each output has a unique input.

• By checking if each input has a unique output.

• By solving the equation for different values.

What is the vertical line test used for?

• To identify the x-intercepts of a graph.

• To determine if a graph is a function.

• To solve quadratic equations.

• To find the slope of a line.

If a vertical line intersects a graph at more than one point, what does it indicate?

• The graph is a quadratic equation.

• The graph is a function.

• The graph is not a function.

• The graph is a linear equation.

Which of the following graphs is not a function?

• A linear graph.

• A parabola.

• A cubic graph.

• A circle.

What does it mean if a vertical line only hits one point on a graph?

• The graph is a quadratic equation.

• The graph is not a function.

• The graph is a function.

• The graph is a relation.

What is required for a graph to be considered a function?

• Each x value must map to multiple y values.

• Each y value must map to only one x value.

• Each x value must map to only one y value.

• Each y value must map to multiple x values.