Multivariable functions | Multivariable calculus | Khan Academy

What is the main difference between a single variable function and a multivariable function?

• A single variable function uses only numbers, while a multivariable function uses only letters.

• A single variable function has one input, while a multivariable function has multiple inputs.

• A single variable function has one output, while a multivariable function has multiple outputs.

• A single variable function is always a straight line, while a multivariable function is always a curve.

When visualizing a multivariable function with two inputs (like x and y), how are these inputs often thought of together?

• As two separate number lines.

• As a single point in a 2D plane.

• As two different colors.

• As a single output number.

What does a 3D graph of a multivariable function typically show?

• The relationship between two inputs and a single output, where the output is represented by height.

• The movement of fluid particles in a space.

• A flat, two-dimensional map with different colors.

• How a 2D shape transforms into another 2D shape.

What are contour lines used for in a 2D visualization of a multivariable function?

• To show the different input values that produce the same output value.

• To represent the speed and direction of movement.

• To draw a three-dimensional shape on a flat surface.

• To indicate the highest and lowest points of the function.