Understanding Relations and Functions

Define a relation in mathematics.

• A relation is a collection of unordered elements.

• A relation is a single element from a set.

• A relation is a mathematical operation that combines two numbers.

• A relation is a set of ordered pairs that associates elements from one set with elements of another set.

What is the difference between a relation and a function?

• A relation can have multiple outputs for a single input, while a function has exactly one output for each input.

• Both relations and functions can have multiple outputs for a single input.

• A relation has no outputs for any input, while a function can have multiple outputs.

• A function can have no outputs for a single input, while a relation has exactly one output.

Give an example of a function and explain why it is a function.

• f(x) = x^2 + 1

• f(x) = sin(x)

• f(x) = 2x + 3

• f(x) = 3x - 5 + x^2

What is the domain of a function?

• The graph of a function.

• The output values of a function.

• The range of a function.

• The set of all possible input values for a function.

What is the range of a function?

• The set of all possible output values of a function.

• The maximum value a function can achieve.

• The average value of a function over its domain.

• The set of all possible input values of a function.

Explain what it means for a function to be one-to-one.

• A function is one-to-one if no two different inputs map to the same output.

• A function is one-to-one if it has at least one input for every output.

• A function is one-to-one if all outputs are unique regardless of inputs.

• A function is one-to-one if it can be graphed as a straight line.

What is the vertical line test? How is it used to determine if a graph represents a function?

• The vertical line test is used to find the area under a curve.

• The vertical line test checks if a graph is symmetrical.

• The vertical line test determines if a graph represents a function by checking if any vertical line intersects the graph at more than one point.

• The vertical line test determines the slope of a graph.

Define an inverse function.

• An inverse function is a function that doubles the output of the original function.

• An inverse function is a function that has no effect when applied to its input.

• An inverse function is a function that only works for linear equations.

• An inverse function is a function that, when composed with the original function, yields the identity function.

How do you find the inverse of a function?

• Multiply x and y, then solve for x.

• Swap x and y, then solve for y.

• Add x and y, then find the derivative.

• Graph the function and reflect it over the y-axis.

What is a composite function?

• A composite function is a single function that cannot be broken down into simpler functions.

• A composite function is a function created by combining two functions, where the output of one function becomes the input of another.

• A composite function is a function that is defined only for positive integers.

• A composite function is a function that only takes one input and produces one output.