Functions

What is the domain of a function?

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

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

• The range of values that the function can take.

• The maximum value that the function can achieve.

Can a function be represented in multiple ways?

• Yes, a function can be represented as a table, graph, equation, or mapping diagram.

• No, a function can only be represented as an equation.

• Yes, but only as a graph or table.

• No, functions cannot be represented in any way.

What is an example of a function?

• f(x) = x + 2, where each input x gives a unique output.

• f(x) = x^2 + 3, which is a quadratic function.

• f(x) = sin(x), which is a trigonometric function.

• f(x) = 1/x, which is a rational function.

What is a one-to-one function?

• A function where each output is associated with exactly one input.

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

• A function that is always increasing or decreasing.

• A function that maps inputs to outputs randomly.

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 maximum and minimum values of the function.

• The slope of the function at a given point.

Is the following graph a function? (A graph that fails the vertical line test)

• Yes, it is a function because it passes the vertical line test.

• No, it is not a function because a vertical line intersects it at more than one point.

• Yes, it is a function because it is a straight line.

• No, it is not a function because it is a curve.

Is the following set of ordered pairs a function? {(1, 2), (1, 3), (2, 4)}

• Yes, because each input corresponds to exactly one output.

• No, because the input '1' corresponds to two different outputs (2 and 3).

• Yes, because all inputs are unique.

• No, because there are no repeated pairs.

What is the vertical line test?

• A method to determine if a graph represents a function by checking if a vertical line intersects the graph at more than one point.

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

• A way to measure the area under a curve in calculus.

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

What is a linear function?

• A function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m and b are constants.

• A function that graphs to a curve and can be expressed in the form f(x) = ax^2 + bx + c.

• A function that has a constant rate of change and can be represented by a polynomial of degree 2.

• A function that does not have a constant rate of change and cannot be expressed in a simple algebraic form.

Is the following mapping diagram a function? (1 -> 2, 1 -> 3, 2 -> 4)

• Yes, because each input corresponds to exactly one output.

• No, because the input '1' corresponds to two different outputs (2 and 3).

• Yes, because all outputs are unique.

• No, because the input '2' does not have a corresponding output.