Answer:
Step-by-step explanation:
Add 81 to both sides:
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Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
To shift vertically n units, we can simply add n to our function. Hence:
So, a vertical shift of 5 units up implies that n=5. So:
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
Or:
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
Answer:
Step-by-step explanation:
First, start out with the parent function:
Now, we look at the transformations, and make the equation.
We see that the graph <u>shifted down 4 units</u>, since the <u>graph's horizontal asymptote</u> is at y = -4.
We see point (0, -3) to point (1, -1). The value of b would be 3. The reason is that when you <u>plug 0 in, you get 1, then 1 - 4 equals 3. (0, -3),</u>
<u>Then, when you plug in 1, you get 3, then 3 - 4 equals -1. This matches up with the graph.</u>
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