Problem 1
Answers:
A) vertical shift down 5
D) horizontal shift right 4
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Step-by-step explanation:
The replacement of x with x-4 means we shift the xy axis 4 units to the left, giving the illusion the curve shifts 4 units to the right. The -5 at the end effectively subtracts 5 from the y coordinate so that's why we shift 5 units down.
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Problem 2
Answers:
A) Vertical stretch
C) Vertical shift up 4
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Step-by-step explanation:
The first 2 indicates we stretch by a factor of 2. So it is twice as tall as before. The x-3 means we shift the curve 3 units to the right. The +4 at the end means we move 4 units up.
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Problem 3
Answer: Choice A) y = 3(x-4)^2 - 2
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Step-by-step explanation:
The 3 makes the graph 3 times taller than before. The x-4 shifts the graph 4 units to the right. The -2 at the end shifts everything 2 units down.
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Problem 4
Answer: Choice B) y = -(x+6)^2
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Step-by-step explanation:
The negative out front is the same as -1 out front. This reflects everything over the x axis. For instance, the point (0, 36) moves to (0,-36). The replacement of x with x+6 shifts everything 6 units to the left.