Describe the transformations from the graph of f(x) = |x| to the graph of g(x). Then graph both functions.
Describe the transformations from the graph of f(x) = |x| to the graphs of g(x) and h(x). Then graph all the three functions.
Describe the transformations from the graph of f(x) = |x| to the graphs of g(x) and h(x). Then graph all the three functions.
Describe the transformations from the graph of f(x) = |x| to the graphs of g(x) and h(x). Then graph all the three functions.
Describe the transformations from the graph of f(x) = |x| to the graph of g(x). Then graph both functions.
In a charity race, a water stand for the runners is halfway between the start and finish lines. The absolute value function y = |(x/8) - 3|models Riley’s distance y in miles from the water stand x minutes into the race. The function y = |(x/10) - 3| models Dean’s distance from the water stand during the same race. Compare Dean’s graph to Riley’s graph. What can you conclude about Dean’s speed?
Identify a, b, and c.
• a = -1 : graph opens downward and width is unchanged
• b = 0 : no horizontal translation
• c = 0 : no vertical translation
Identify a, b, and c.
no horizontal translation
no vertical translation
no horizontal translation
no vertical translation
Identify a, b, and c.
width is unchanged
translated 2 units left
no vertical translation
width is unchanged
translated 2 units right
no vertical translation
Identify a, b, and c.
width is unchanged
no horizontal translation
translated 2 units up.
width is unchanged
no horizontal translation
translated 2 units down
Identify a, b, and c.
g(x) = 2|x + 1| = 2|x – (–1)| + 0.
• a = 2 : graph is narrower
• b = –1 : translated 1 unit left
• c = 0 : no vertical translation
Identify a, b, and c.
g(x) = -|x - 3| + 2 = -1|x – 3| + 2.
• a = -1 : graph opens downward and width is unchanged
• b = 3 : translated 3 units right
• c = 2 : translated 2 units up
y = |(x/8) - 3| is graphed in blue.
y = |(x/10) - 3| is graphed in red. Both graphs start at the same point, but Dean’s graph is translated to the right. It takes him more time to reach the water stand and to finish the race. Therefore, he is running more slowly than Riley.
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