Section 3.6 Functions 275 a. In an equation, we do this by substituting the variable with the given number. b. In a table or graph, we find the ordered pair in the table or on the graph with the given x value. The y-value of this ordered pair is the value we need. 5. Linear equations in two variables of the form y = mx + b can be written in function notation as f (x) = mx + b. Equations of the form Ax + By = C must be solved for y before they can be written in function notation. Vertical lines are not functions. 6. Functions occur in many real-world situations. It is important to understand from the problem what the input and output of the function represent. GRAPHING CALCULATOR SKILLS The graphing calculator can assist us in evaluating functions when the function is given in terms of an equation. Input the function into the calculator to find the requested information. Example: Find f (0) if f (x) = ux - 4u. Solution: Input the equation into the calculator and use the Table or TRACE feature to find the y-value. MATH ENTER T u n 2 4 ) ENTER Use the Table to find the y-value when x = 0. 2nd RA H Graph the equation and use the TRACE feature to find the point that has an x-value of 0. RA H TRA E So, f (0) = 4. �� ���������������� �������� EXERCISE SET Write About It! Use complete sentences in your answer to each exercise. 1. Define a relation and its domain and range. 2. How do we determine if a relation is a function? 3. What is the vertical line test? 4. Define a function. 5. What is function notation? 6. What is the difference between an equation of a line and a linear equation in two variables in function notation? Determine if each statement is true or false. If a statement is false, explain why it is false. 7. If f (3) = 5, then (3, 5) is a point on the graph of the function f. 8. If f (0) = -7, then the x-intercept is (-7, 0). 9. If f (8) = 0, then the y-intercept is (0, 8). 10. A relation is always a function. 11. If any vertical line intersects a graph in more than one point, the graph represents a function. 12. A relation always has a domain and range. Practice Makes Perfect! Express each relation in Exercises 13–16 as a set of ordered pairs. State the domain and range of each relation. (See Objective 1.) 13. The following table shows the 2009 total health expenditure per capita in the selected countries. (Source: http://www.who.int/en) Countries Per Capita Canada $4400 France $4800 Italy $3300 Japan $3300 Republic of Korea $1100 United Kingdom $3300 United States $7400
hendricks_beginning_algebra_1e_ch1_3
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