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2 answers:
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Answer:
Step-by-step explanation:
If we have a linear function and we multiply the input of the function, we aren't really <em>changing</em> the values of the function, we're changing the rate at which those values are reached.
E.g. if you look at the attached picture, we have and
, which is just
. The value when the red line is x = 1 is half that of the value of the blue line when x = 1.
The values of the f(2x) line are reaching the values of f(x) twice as fast, meaning it has a slope of twice as much. However, it still grows through the same intercept.
If you're interested in the calculus behind this, look up the chain rule of derivatives.
However, when you start changing the output of the function, you're changing the entire equation. It's not the same line anymore.
Answer:
A
Step-by-step explanation:
The common ratio of a geometric sequence is found by dividing any term (after the first term) by the term before it.
Let's take the 2nd term, 2, and divide it by the previous term, which is 8.
So
Thus, the common ratio = 1/4
Choice A is right.