Describe the sequence of transformations that are required to graph based on .a.)The graph is shifted to the right by 3 units, reflected around the x-axis, compressed vertically, and shifted down 5 units.b.)The graph is shifted to the right by 3 units, compressed vertically, and shifted down 5 units.c.)The graph is shifted to the left by 3 units, reflected around the x-axis, stretched vertically, and shifted up 5 units.d.)The graph is shifted to the left by 3 units, reflected around the x-axis, compressed vertically, and shifted down 5 units.
Question
Describe the sequence of transformations that are required to graph based on .a.)The graph is shifted to the right by 3 units, reflected around the x-axis, compressed vertically, and shifted down 5 units.b.)The graph is shifted to the right by 3 units, compressed vertically, and shifted down 5 units.c.)The graph is shifted to the left by 3 units, reflected around the x-axis, stretched vertically, and shifted up 5 units.d.)The graph is shifted to the left by 3 units, reflected around the x-axis, compressed vertically, and shifted down 5 units.
Solution
a.) To graph the function based on the given transformations, you would first shift the graph 3 units to the right. This means every point on the graph is moved 3 units to the right. Next, you would reflect the graph around the x-axis, which means you flip the graph over the x-axis. Then, you would compress the graph vertically, which means you shrink the graph towards the x-axis. Finally, you would shift the graph down 5 units, which means every point on the graph is moved 5 units down.
b.) To graph the function based on these transformations, you would first shift the graph 3 units to the right. Then, you would compress the graph vertically. Finally, you would shift the graph down 5 units.
c.) To graph the function based on these transformations, you would first shift the graph 3 units to the left. Then, you would reflect the graph around the x-axis. Next, you would stretch the graph vertically, which means you pull the graph away from the x-axis. Finally, you would shift the graph up 5 units.
d.) To graph the function based on these transformations, you would first shift the graph 3 units to the left. Then, you would reflect the graph around the x-axis. Next, you would compress the graph vertically. Finally, you would shift the graph down 5 units.
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