[THESE ARE NOT THE RIGHT ANSWERS I JUST GUESSED]
1 answer:
The parent function of the function represented in the table is <u>exponential</u>.
- Note if you subtract 10 from each output, you get
.
If function f was translated down 4 units, the <u>f(x)</u> values would be <u>decreased by 4</u>.
- See attached image.
A point on the table for the transformed function would be <u>(4, 87).</u>
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Since , by the remainder theorem this means that <em>x</em> - 6 divides <em>f(x)</em> exactly. This means there are constants <em>a</em>, <em>b</em>, and <em>c</em> such that
Multiplying both sides by <em>x</em> - 6 gives
Then <em>a</em>, <em>b</em>, <em>c</em> satisfy
and solving this system gives <em>a</em> = 2, <em>b</em> = -7, and <em>c</em> = 3.
So, we have
The quadratic term can be factored as
which leaves us with
so that the zeros of <em>f(x)</em> are 6, 1/2, and 3.