Behaviors of Linear Functions
Question 3 From Assignment 0
In this question I will draw different graphs on the same set of axes and describe them on how they behave. The first one is y=4(x-2). This is a straight line or linear function with a positive slope equals 4. It has a y-intercept at (0,-8) and x-intercept at (2,0) It is represented on the graph by the purple color.
Figure 1 Set of Graphs
The second one is y=3(x-2). This is also a straight line with slope a slope of 3, and it has intercepts at (2,0) and (0,-6) respectively. It is represented in the set of graphs by the red color. The next one is y=2(x-2). It is another linear function with the inercepts at (2,0) and (0,-4) and it is shown on the graph by the blue color. The next function is y=1(x-2). This is also linear function with slope equals 1 and it has intercepts at (-2,0) and (0,-2). It is represented with green color. The next one is y=0(x-2). Since we are multiplying by zero here, the functuion y=0 (zero property). This represents the origin (0.0) and it will be just a point, The next function is y=-1(x-2). The slope of this one is negative and its intercepts are (2,0) and (0,2), and it is represented by the yellow color. Another one is y=-2(x-2). This also is a linear function but it has a negative slope equals to -2. Its intercepts are (2,0) and (0,4) respectively. It has a tan color.The next function is y=-3(x-2). This is also linear with negative slope -3 and intercepts are (2,0) and (0,6). Iy is the black straight line.The last one is y=-4(x-2). It is a linear function as the previous ones with a negative slope -4 with x and y-inercepts at (2,0) and (0,8) respectively. It is in white color.
Now we need to look at all slopes of the functions and its intercepts and try to observe any pattern that depicts either similarities or differences. For the positive slopes we had the following intercepts:
+4 (2,0), (0,-8), +3 (2,0), (0,-6), +2 (2,0), (0,-4) +1 (2,0), (0,-2) 0 (0,0), (0,0). For the negative slopes wed had the following intercepts: -4 (2.0), (0,8) -3 (2,0). (0,6), -2 (2,0),(0,4) -1 (2,0),(0,2).
1)All functions were even functions and all of its intercepts were even
2)All x-intercepts are located at one point (2,0).
3)The y-intercepts are positive for the negative slopes and negative for the positive slopes.