week 5 Relations and Functions

week 5 Relations and Functions

Your initial post should be at least 250 words in length


In this discussion, you will be assigned two equations where you will complete a variety of math work related to mathematical functions. Read the following instructions in order and view the attached example to complete this discussion.


Do ONLY problem 24 and 38 attached 


Problem 38 Sketch the graph of each function, and state the domain and range.See the Strategy for graphing y = af(x − h) + 

When graphing a function containing more than one transformation, perform the transformations in the following order:

Strategy for graphing y = af(x − h) + k

To graph y = af(x – h) + k, start with the graph of y = f(x) and perform

  1. Horizontal translation    (right for h > 0 and left for h < 0)
  2. Stretching/shrinking    (stretch for a > 1 and shrink for 0 < a < 1)
  3. Reflection    (reflect in x-axis for a < 0 or y = −f(x))
  4. Vertical translation    (up for k > 0 and down for k < 0).


Note that the order in which you reflect, stretch, or shrink does not matter. It does matter that you do vertical translation last. For example, if y = x2 is reflected in the x-axis and then moved up two units, the equation is y = −x2+ 2. If it is moved up two units and then reflected in the x-axis, the equation is y = −(x2 + 2) or y = −x2 − 2.A change in the order produces different functions.



There are many ways to go about solving math problems. To solve this problem, you will be required to do some work that will not be included in the discussion point.

  • First, graph your functions so that you can clearly describe the graphs in your post. Your graph itself is not required in your post, although a discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.
  • Mention any key points on the graphs, including intercepts, vertex, or start/end points. Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.
  • Discuss the general shape and location of each of your graphs.
  • State the domain and range for each of your equations. Write them in interval notation.
  • State whether each of the equations is a function or not giving your reasons for the answer.
  • Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.
  • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.
    • Function
    • Relation
    • Vertical Line test
    • Transformation
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