Relations, Functions, & Linear vs. Nonlinear

What is a nonlinear function?

• A function that forms a straight line when graphed.

• A function that does not form a straight line when graphed, indicating a variable rate of change.

• A function that has a constant rate of change.

• A function that can be represented by a linear equation.

What is a function?

• A function is a type of equation that has multiple outputs for a single input.

• A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).

• A function is a graphical representation of data points.

• A function is a method of solving algebraic expressions.

Can a function have multiple outputs for a single input?

• Yes, a function can have multiple outputs for a single input.

• No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

• It depends on the type of function being used.

• Only in certain mathematical contexts.

What is the vertical line test?

• A method to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.

• A technique used to find the slope of a line in a graph.

• A way to measure the height of a graph at various points.

• A test to check if a graph is symmetrical about the y-axis.

What is the range of a function?

• The set of all possible input values (x-values) that the function can accept.

• The set of all possible output values (y-values) that the function can produce.

• The difference between the highest and lowest values of the function.

• The slope of the function at a given point.

What is a linear function?

• A function that can be graphically represented as a straight line, with a constant rate of change.

• A function that has a variable rate of change and can be represented by a curve.

• A function that only includes positive values and cannot be negative.

• A function that is defined by a quadratic equation.

What is the domain of a function?

• The set of all possible input values (x-values) for which the function is defined.

• The set of all possible output values (y-values) of the function.

• The maximum value that a function can take.

• The minimum value that a function can take.

How can you determine if a relation is a function?

• A relation is a function if no x-value is repeated with different y-values.

• A relation is a function if every y-value has a unique x-value.

• A relation is a function if it contains at least one ordered pair.

• A relation is a function if it is represented by a straight line.

What is a constant function?

• A function that always returns the same value, regardless of the input.

• A function that changes its output based on the input.

• A function that has no output at all.

• A function that can only take one specific input.

What is the slope of a linear function?

• The ratio of the change in y to the change in x, representing the steepness of the line.

• The distance between two points on the line.

• The y-intercept of the line.

• The angle at which the line intersects the x-axis.