Category: Tables, Graphs, Functions

Introduction Many real-world situations involve two variable quantities in which one quantity depends on the other. The quantity that depends on the other quantity is called the dependent variable, and the quantity it depends on is called the independent variable. The values of variables are used in tables and in plotting graphs. In this lesson,…

Introduction In this lesson, we solve real world problems which are modeled by an equation. The equation describing the problem is written and its graph is plotted. Example 1 Jenny has savings of 42andearns7 for each hour of lawn mowing. If y is the total amount with Jenny and x is the number of hours he…

Introduction In this lesson, given a table of values, graphs are plotted from ordered pairs and equations are written. Suppose we are given a table showing x and y values. The independent variable is represented by x and the dependent variable is represented by y and we have the ordered pairs of x,y. Example 1 Plot…

Introduction In this lesson, given a real-world situation, we write a function to model the problem and then evaluate it for a particular situation or value. Example 1 Moe has savings of 70andheearns5 for each hour of lawn mowing. If A is the amount with Moe and h is the number of hours he works, write…

Introduction In this lesson, we have two-step functions with decimals modeling real world problems. In such a case we find outputs of those functions. Example 1 The amount that Jane has is given by the function Ax = 0.8x + 18, where x is her allowance in dollars. What is the amount she has if her…

Introduction In this lesson, we have one-step functions modeling real world problems. In such cases we find outputs of those functions. Example 1 After eating at a restaurant, Joe, Tom, Bill and Sunny decided to divide the bill evenly. If the total bill given by the function Ax = 4x amounted to $136, how much should…

Introduction A line graph is mostly used to show change over time as a series of data points connected by line segments on the coordinate plane. The line graph therefore helps to find the relationship between two data sets, with one data set always being dependent on the other set. Line graphs are drawn such…

Introduction We graph a line whose equation is given, say for example y = 3x. We need at least two points or ordered pairs to graph the line. First we choose some x values. Then we evaluate y = 3x for each value of x. For example for x = 0, y = 30 = 0;…

Introduction In this lesson, we find the function rule given a table of ordered pairs. We first identify the input and the output variables and their values. We find if the function is increasing or decreasing. If the function is increasing, it means there is either an addition or multiplication operation between the two variables.…

Introduction In this lesson, we fill in a table with x and y values given a function rule with two-step rules. Usually the function rule is a linear equation in x and y. By giving different values to the independent variable x, corresponding values of dependent variable y are found. These x and y values…