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Understanding Functions: Domain, Range, and Piecewise Equations

This quiz focuses on key concepts of functions, including determining the domain and range of absolute value and piece-wise functions, as well as recognizing their graphical representations. Students will learn how to express absolute value functions as piece-wise equations and how to derive the equations from graphs. Additionally, we'll explore linear functions, slopes, and how to identify parallel and perpendicular lines. This comprehensive guide includes practice problems from various homework assignments to reinforce understanding.

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Understanding Functions: Domain, Range, and Piecewise Equations

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  1. 1.3 Functions • HW Pg. 42 #1 – 45 odd Quiz Thursday • Determine the domain and range.

  2. 1.3 Functions Absolute Value Function Piece-wise Functions How does the equation change from a basic absolute value? Write it as a Piece-wise Function. • What does an absolute value function look like? • What is the piece-wise equation for an absolute value function?

  3. 1.3 Functions Write the Piece-wise equation from the graph.

  4. 1.3 Functions Graph the Piece-wise equation.

  5. Questions on HW • HW #1 Pg. 11 #11 – 24 Pg. 21 #7 – 10 • HW #2 Pg. 21 #20 – 29 Pg. 30 #1 – 30 • HW #3 Pg. 30 – 32 #31 – 53 all

  6. 1.4 Linear Functions and Inequalities Slope Find the slope from the given information. (-3, 2) (-1, -2) (1, 2) (-3, 2) (4, -5) (4, 5) (-1, 2) (4, -2) • The slope of a line through two non-vertical points (x1, y1) and (x2, y2) is given by:

  7. 1.4 Linear Functions and Inequalities Parallel and Perpendicular Horizontal and Vertical Lines Horizontal lines: Vertical lines: Find an equation of the line which passes through the points (5, 7) and (5, -8). • Parallel slopes are: • Perpendicular slopes are: • Determine whether the following sets of points are parallel, perpendicular or neither: (-5, 2),(2, 1) and (5, 3),(4, -10)

  8. 1.4 Linear Functions and Inequalities Slope-Intercept Form Point-Slope Form You can find the equation of a line using the slope and one ordered pair (a point). Find an equation of the line which passes through the point (5, -2) and has a slope of –½. • The graph of a straight line is easily described as: • Re-write the equation 3x + 5y = 12 to find the slope and y – intercept. Sketch a complete graph.

  9. 1.4 Linear Functions and Inequalities General Form Practice Find an equation of the line which passes through the point (4, -3) and is perpendicular to the line 2x – 5y = 20. Find an equation of the perpendicular bisector of the segment between the points (6, -3) and (2, 5). • Also known as Standard Form: • Given that A, B, and C are whole numbers • Given that A is positive • Rewrite y = ¼x – 7 in general form.

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