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Chapter 8 More on Functions and Graphs. § 8.1 Graphing and Writing Linear Functions.

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Presentation on theme: "Chapter 8 More on Functions and Graphs. § 8.1 Graphing and Writing Linear Functions."— Presentation transcript:

1 Chapter 8 More on Functions and Graphs

2 § 8.1 Graphing and Writing Linear Functions

3 Martin-Gay, Beginning and Intermediate Algebra, 4ed 33 Identifying Linear Functions  By the vertical line test, we know that all linear equations except those whose graphs are vertical lines are functions.  Thus, all linear equations except those of the form x = c (vertical lines) are linear functions. Linear Functions

4 Martin-Gay, Beginning and Intermediate Algebra, 4ed 44 Let x = 4. f (4) = = 6 S implify the right side. One solution is (4, 6). Graph the linear function f (x) = x + 3. f (4) = (4) + 3 R eplace x with 4. Graphing Linear Functions Example: Continued.

5 Martin-Gay, Beginning and Intermediate Algebra, 4ed 55 For the second solution, let x = 0. f (0) = = 3 S implify the right side. So a second solution is (0, 3). Graph the linear function f (x) = x + 3. f (0) = (0) + 3 R eplace x with 0. Graphing Linear Functions Example continued: Continued.

6 Martin-Gay, Beginning and Intermediate Algebra, 4ed 66 For the third solution, let x = – 4. f (– 4) = – = 0 S implify the right side. The third solution is ( – 4, 0). Graph the linear function f (x) = x + 3. f ( – 4) = ( – 4) + 3 Replace x with – 4. Example continued: Graphing Linear Functions Continued.

7 Martin-Gay, Beginning and Intermediate Algebra, 4ed 77 Plot all three of the solutions (4, 6), (0, 3) and (– 4, 0). x y (4, 6) (0, 3) (– 4, 0) Draw the line that contains the three points. Graphing Linear Functions Example continued:

8 Martin-Gay, Beginning and Intermediate Algebra, 4ed 88 Example: Find an equation of the line whose slope is 5 and contains the point (4,  3). Write the equation using function notation. m = 5, x 1 = 4, y 1 =  3 Writing Linear Functions y – y 1 = m(x – x 1 ) y – (– 3) = 5(x – 4) y + 3 = 5x – 20 y = 5x – 23 Substitute the values for m, x 1, and y 1. Simplify and distribute. Subtract 3 from both sides. f (x) = 5x – 23 Replace y with f (x).

9 Martin-Gay, Beginning and Intermediate Algebra, 4ed 99 Example: Write a function that describes the line containing the point (4, 1) and is perpendicular to the line  y =  5x + 20 Writing Linear Functions Solve the equation for y to find the slope from the slope-intercept form. 5 is the slope of the line perpendicular to the one needed. 5x – y = 20 y = 5x  20 As perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we want is Continued.

10 Martin-Gay, Beginning and Intermediate Algebra, 4ed 10 Example: Write a function that describes the line containing the point (4, 1) and is perpendicular to the line Writing Linear Functions y – y 1 = m(x – x 1 ) Substitute the values for m, x 1, and y 1. Simplify and distribute. Subtract 1 from both sides. Replace y with f (x). 5x – y = 20 m =, x 1 = 4, y 1 = 1 y – (1) = (x – 4) y + 1 = x y = x f (x) = x


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