1.8 Graphs and Functions A function is a relationship between input and output. In a function, the output depends on the input. There is exactly one output for each input. A function is graphed using a coordinate system. – It is formed by the intersection of two number lines, the horizontal axis and the vertical axis.

Coordinate System

Each input x and its corresponding output y can be represented on a graph using ordered pairs. An ordered pair is a set of numbers, or coordinates, written in the form (x, y). The x value, called the x-coordinate, corresponds to the x-axis and the y value, or y- coordinate, corresponds to the y-axis.

Identify Coordinates Refer to the application above. Name the ordered pair at point C and explain what it represents. Point C is at 2 along the x-axis and about 80 along the y-axis. So, its ordered pair is (2, 80). This represents 80% normal blood flow 2 days after the injury.

Variables In Example 1, the percent of normal blood flow depends on the number of days from the injury. Therefore, the number of days from the injury is called the independent variable, or quantity, and the percent of normal blood flow is called the dependent variable or quantity. Usually the independent variable is graphed on the horizontal axis and the dependent variable is graphed on the vertical axis.

Independent and Dependent Variables Identify the independent and dependent variables for each function. a.In general, the average price of gasoline slowly and steadily increases throughout the year. Time is the independent variable as it is unaffected by the price of gasoline, and the price is the dependent quantity as it is affected by time. b.The profit that a business makes generally increases as the price of their product increases. In this case, price is the independent quantity. Profit is the dependent quantity as it is affected by the price.

Analyze Graphs The graph represents the speed of a school bus traveling along its morning route. Describe what is happening in the graph. At the origin, the bus is stopped. It accelerates and maintains a constant speed. Then it begins to slow down, eventually stopping. After being stopped for a short time, the bus accelerates again. The starting and stopping process repeats continually.

Analyze Graphs Identify the graph that represents the altitude of a space shuttle above Earth, from the moment it is launched until the moment it lands. Before it takes off, the space shuttle is on the ground. It blasts off, gaining altitude until it reaches space where it orbits Earth at a constant height until it comes back to Earth. Graph A shows its situation.

Draw Graphs See Example 4 on p. 45.

A set of ordered pairs, like those in Example 4, is called a relation. The set of the first numbers of the ordered pairs is the domain. The domain contains all values o the independent variable. The set of second numbers of the ordered pairs is the range of the relation. The range contains all values of the dependent variable.

Domain and Range See Example 5 on p. 45.