Problem 7
Consider the general template
g(x) = a*sqrt(x-h) + k
and compare it to the general parent function
f(x) = sqrt(x)
We have the following variables: a, h and k
They are defined as such:
- a = handles the vertical stretch and if any reflections occur. If a > 0, then the curve goes upward; if a < 0, then the curve goes downward. Going from positive to negative, or vice versa, is a reflection over the x axis.
- h = handles the left and right shift. If h > 0, then you shift right. If h < 0, then you shift left.
- k = handles the up and down shifting. If k > 0, then you shift up. If k < 0, then you shift down.
For this problem, we have
Since g(x) = sqrt(x+4)+3 is the same as g(x) = 1*sqrt(x - (-4)) + 3
With a = 1, we know that the curve moves upward. Compared to the parent graph y = sqrt(x), which also goes upward, no reflection has been done over the x axis.
The h = -4 means we shift 4 units to the left
The k = 3 means we shift 3 units up
Answer: Shift the parent function 4 units to the left and 3 units up
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Problem 8
We'll use the ideas mentioned in problem 7. They'll also be used for problems 9 and 10 as well.
For problem 8, we have
- a = 1
- h = -4 = shift 4 units to the left
- k = -2 = shift 2 units down
Answer: Shift the parent function 4 units to the left and 2 units down.
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Problem 9
This time we have
Answer: Shift the parent function 4 units to the right and 3 units down
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Problem 10
So far, all of the 'a' values have been positive 1. This means that there hasn't been any reflection or vertical stretching going on.
This time we have a = -1 instead of a = 1.
So we will reflect over the x axis along with the shiftings similar to the ones that occurred with the previous problems.
Answer: Reflect the parent function over the x axis, shift 4 units to the right, and shift 2 units up
