Cartesian Coordinate System Quiz

A system that uses two perpendicular lines (axes) to define the position of a point in a plane, using ordered pairs of numbers (x, y).

The point where the x-axis and y-axis intersect in a Cartesian coordinate system.

The first number in an ordered pair (x, y) that represents the distance of a point from the y-axis.

The second number in an ordered pair (x, y) that represents the distance of a point from the x-axis.

The area of the Cartesian plane where both the x and y coordinates are positive.

The area of the Cartesian plane where the x-coordinate is negative and the y-coordinate is positive.

The area of the Cartesian plane where both the x and y coordinates are negative.

The area of the Cartesian plane where the x-coordinate is positive and the y-coordinate is negative.

A function where each element in the domain maps to a unique element in the codomain. In other words, no two different inputs can produce the same output.

A function where every element in the codomain has at least one corresponding element in the domain. In other words, every possible output is achieved by at least one input.

A function that is both one-to-one and onto. This means each input maps to a unique output, and every possible output is achieved by exactly one input.

A way to visually determine if a function is one-to-one. If any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

The set of all possible outputs of a function.

A function where the output is calculated by squaring the input.

A function where the output is calculated by multiplying the input by 2 and then subtracting 1.

A function where the output is calculated by taking the square root of the input.

The graph of a linear function is a straight line that can be either increasing, decreasing, or horizontal.

The slope determines the steepness and direction of the line. A positive slope means the line rises from left to right, a negative slope means it falls from left to right, and a zero slope means the line is horizontal.

The point where the line crosses the y-axis. It is found by setting x = 0 and solving for y.

The point where the line crosses the x-axis. It is found by setting y = 0 and solving for x.

The range of a linear function is the set of all real numbers. This means the graph will continue infinitely in both directions.

The graph is continuous, meaning there are no breaks or holes in the line.

A linear function is increasing if its slope is positive, and decreasing if its slope is negative.

A function is onto (or surjective) if every element y in the codomain has at least one corresponding element x in the domain such that f(x) = y. In simpler terms, the function 'hits' all values in the codomain.

As x approaches positive or negative infinity, f(x) also approaches positive or negative infinity, depending on the sign of the slope.

A function is a one-to-one correspondence (or bijective) if it is both one-to-one and onto. This means every element in the codomain is mapped to by exactly one element in the domain.

The graph of a function visually represents the relationship between input values (domain) and output values (range). Each point on the graph represents a pair of input and output values.

The domain of a function is the set of all possible input values for which the function is defined. It represents the range of values that can be put into the function.

A linear function is a function whose graph is a straight line. It can be represented in the form y = mx + c, where 'm' is the slope and 'c' is the y-intercept.

A constant function is a function whose output value is the same for all input values. Its graph is a horizontal line.

The highest or lowest point on the graph of a quadratic function, representing the maximum or minimum value of the function.

A method of rewriting a quadratic function in the form f(x) = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

For the general form of a quadratic function f(x) = ax^2 + bx + c, this value determines if the parabola opens upwards (a > 0) or downwards (a < 0).

The x-value where the vertex of the parabola occurs.

The points where the graph of the quadratic function intersects the x-axis (y = 0).

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

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

The y-coordinate of the vertex, representing the maximum or minimum value of the function.

The solutions or zeros of a quadratic equation are the x-intercepts of its graph, where the graph crosses the x-axis, making the function zero.

The concavity of a quadratic function tells us whether the parabola opens upwards (concave up) or downwards (concave down).

The vertex of a quadratic function is the highest or lowest point on the parabola, depending on the concavity.

The intercepts of a quadratic function are the points where the graph crosses the x-axis (x-intercepts) and the y-axis (y-intercept).

A quadratic equation has two real solutions if its graph crosses the x-axis at two distinct points.

A quadratic equation has one real solution if its graph touches the x-axis at one point (the vertex) and doesn't cross it.

A quadratic equation has no real solutions if its graph does not intersect or touch the x-axis.

Solving a quadratic inequality graphically involves determining the intervals on the x-axis where the function is either greater than or less than zero, based on the inequality symbol.