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ALGEBRA II HONORS/GIFTED @

This section covers the concept of families of functions and explores the properties of absolute value functions. It includes discussions on the parent graph, shifts, reflections, and transformations of these functions.

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ALGEBRA II HONORS/GIFTED @

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  1. ALGEBRA II HONORS/GIFTED @ SECTION 2-6 : FAMILIES OF FUNCTIONS SECTION 2-7 : ABSOLUTE VALUE FUNCTIONS

  2. ABSOLUTE VALUE FUNCTION : is defined by the equation or Take out your and type into y1, . Hit zoom6 and graph. You should get vertex This is the parent graph of . It is a V shaped graph symmetric about the y-axis. The minimum value is called the vertex.

  3. Type into y2 : Type into y3 : How does this graph compare with the parent graph? How does this graph compare with the parent graph? The graph shifts one unit to the right. The graph shifts two units to the right. Predict what happens to in relation to the parent graph? Shifts three units to the right.

  4. Predict what happens to the graph of in relation to the parent graph. Shifts four units to the left. So, as long as h ≠ 0, the graph of moves the parent graph h units horizontally. Now, clear out the y2 and y3 in your graphing calculator. Type into y2 : . What happens to this graph in relation to the parent graph in y1? Shifts the graph down one unit.

  5. Type into y3 : . What happens to this graph in relation to the parent graph? Shifts the graph up four units. TRANSFORMATION : changes a graph’s size, position, shape, or orientation. TRANSLATION : is a transformation that shifts a graph horizontally and/or vertically only. Moves the parent graph x units horizontally and k units vertically.

  6. Given the parent graph , graph : Identify the axis of symmetry for each graph. What just happened to the parent graph? The graph is stretched by a factor of two.

  7. VOCABULARY Reflection : flips the graph across a line such as the x- or the y-axis. Each point on the graph of the reflected function is the same distance from the line of reflection as its corresponding point on the graph of the original function. (See page 101 of your textbook.) Vertical Stretch : multiplies all y values of a function by the same factor greater than 1. Vertical Compression : multiplies all y values of a function by a factor between 0 and 1. See the bottom of page 102 for a summary.

  8. Now, let’s extend what we have just learned to other graphs. 7) Given f(x) = x. Make one change in the equation to create a horizontal shift up 4 units. Answer : f(x) = x + 4 8) What is the equation of the graph y = -x2 translated down 3 units? Answer : y = -x2 - 3 9) What transformations change were made from f(x) to g(x)? f(x) = x3 g(x) = (x + 4)3 - 1 Answer : a horizontal translation 4 units to the left and a vertical translation 1 unit down.

  9. 10) The function f(x) = 8x. The function g(x) is f(x) vertically compressed by a factor of 0.5 and reflected in the x-axis. What is the function rule for g(x)? Answer : f(x) = -4x 11) Let g(x) be the reflection of f(x) = 2x – 7 in the y-axis. What is the rule for g(x)? Answer : g(x) = -2x - 7

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