Relations and Functions

Relations and Functions

Graph each quadratic function, and state its domain and range. 

f (x) = x² - 4

Sketch the graph of each function, and state the domain and range.

1. 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

   Your initial post should be at least 250 words in length.