Features of Functions

What is a minimum point on a graph?

• A point where the function value is greater than the values around it.

• The highest point on the graph of a function.

• A point where the function value is less than or equal to the values around it.

• A point where the graph intersects the x-axis.

What is a y-intercept?

• The point where the graph intersects the x-axis, represented as (x, 0).

• The point where the graph of a function intersects the y-axis, represented as (0, y).

• The slope of the graph at the origin.

• The maximum point of the graph.

What is a function?

• A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

• A function is a mathematical operation that combines two or more numbers to produce a single number.

• A function is a type of graph that represents data points in a coordinate system.

• A function is a programming construct that allows for the execution of a block of code multiple times.

What does it mean for a function to be increasing?

• A function is increasing on an interval if, as the input values increase, the output values also increase.

• A function is increasing if its graph slopes downward from left to right.

• A function is increasing if it has a positive y-intercept.

• A function is increasing if it oscillates between positive and negative values.

What is the domain of a function?

• The range of possible output values of the function.

• The complete set of possible values of the independent variable (input) for which the function is defined.

• The graphical representation of the function on a coordinate plane.

• The maximum and minimum values that the function can take.

What does it mean for a function to be decreasing?

• A function is increasing on an interval if, as the input values increase, the output values increase.

• A function is constant on an interval if, as the input values increase, the output values remain the same.

• A function is decreasing on an interval if, as the input values increase, the output values decrease.

• A function is undefined on an interval if, as the input values increase, the output values cannot be determined.

What is an interval in the context of functions?

• A specific point on the x-axis where the function is defined.

• A range of values on the x-axis or y-axis that defines where a function is increasing, decreasing, or constant.

• A method to calculate the slope of a function.

• A type of function that only includes positive values.

What is the significance of the vertex in a quadratic function?

• The vertex is the point where the parabola intersects the x-axis.

• The vertex is the highest or lowest point of a parabola, representing the maximum or minimum value of the function.

• The vertex indicates the direction in which the parabola opens.

• The vertex is the midpoint of the parabola's base.

What is a quadratic function?

• A polynomial function of degree 1, typically represented in the form y = ax + b.

• A polynomial function of degree 2, typically represented in the form y = ax^2 + bx + c.

• A polynomial function of degree 3, typically represented in the form y = ax^3 + bx^2 + cx + d.

• A linear function represented in the form y = mx + b.

What is a continuous function?

• A function that can be graphed without lifting the pencil from the paper, meaning there are no breaks or holes in the graph.

• A function that has a finite number of discontinuities.

• A function that can only be graphed in a straight line.

• A function that oscillates between two values without settling.