Functions and Their Evaluations

A function is a set of ordered pairs where each input (x-value) has exactly one output (y-value). It can be represented as a graph, table, or equation.

To evaluate a function, substitute the given input value for the variable in the function's equation and then simplify.

The slope of a line represents how steep or flat the line is. It's calculated as the change in y divided by the change in x.

The y-intercept is the point where the line crosses the y-axis.

A system of equations is a set of two or more equations with the same variables. The solution is a point (x, y) that satisfies all equations in the system.

The solution to a system of equations can be found by graphing the equations and identifying the point of intersection.

The elimination method involves adding or subtracting equations in a system to eliminate one variable, then solving for the remaining variable.

The substitution method involves solving one equation for one variable, then substituting the expression into the other equation to solve for the remaining variable.

The difference between the upper quartile (Q3) and the lower quartile (Q1) of a dataset. It represents the spread of the middle 50% of the data.

A function where the output value is multiplied by a constant factor for each unit increase in the input value. It exhibits exponential growth or decay.

A model that describes the value of an asset decreasing over time at a constant rate. It is commonly used to calculate depreciation of assets.

A model that represents the value of an investment increasing over time at a constant rate. It is commonly used to calculate compound interest.

A mathematical representation of the relationship between an input (typically time) and an output (typically the value of an investment) in an exponential function.

A mathematical representation of a situation where a quantity increases or decreases at a constant rate, where the change is multiplied by a constant factor for each unit increment of the input.

The rate at which an investment grows or an asset depreciates, expressed as a percentage.

A model that describes the decrease in value of an asset over time due to wear and tear, obsolescence, or other factors.

The difference between the highest and lowest values in a dataset.

The value that represents the 50th percentile in a dataset. Half of the values are less than the median, and half are greater.

The value that occurs most frequently in a dataset.

The average of all the values in a dataset. To calculate it, you add all the values together and divide by the total number of values.

The first quartile (Q1) is the 25th percentile of a dataset, meaning 25% of the data falls below it. The third quartile (Q3) is the 75th percentile, with 75% of the data falling below it.

A measure of how far a data point is from the mean, expressed in standard deviations. A positive z-score indicates the data point is above the mean, while a negative z-score indicates the data point is below the mean.

A statistical measure that describes the strength of the linear relationship between two variables. It ranges from -1 to 1, with values closer to 1 indicating a strong positive relationship, values closer to -1 indicating a strong negative relationship, and values close to 0 indicating a weak or no relationship.