3 Answers:
- Choice B) As x decreases, y decreases
- Choice C) As x increases, y approaches 0
- Choice F) The function is an increasing function
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Explanation:
The graph has a negative y-intercept. So for example, we could have a y intercept of (0,-1) or (0,-2). The x value is always 0, and in this case, the y coordinate is some negative number.
Due to the negative y intercept, this means the function curve is below the x axis at this point. The common ratio r, such that 0 < r < 1, tells us that the exponential function is decreasing in absolute value. Let's say the y intercept was (0,-10) and the common ratio was r = 0.5
The common ratio of r = 0.5 means the second term is r*(first term) = 0.5*(-10) = -5, and the third term is r*(second term) = 0.5*(-5) = -2.5
The terms: -10, -5, -2.5 show us that they are decreasing in absolute value, but in terms of a graph, they are going upward toward zero.
So that's why as x increases, so does y (which makes it an increasing function). And y is approaching y = 0. However, it never actually gets to y = 0.
On the flip side, if x is decreasing, then y is also decreasing. Both x and y increase or decrease together in any increasing function. A decreasing function would have x increase while y decreases, or vice versa, meaning they go in opposite directions.
