The functions $f$ and $g$ are defined as follows: \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}
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Answer:
On a coordinate plane, a curve is level at y = -1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).
Step-by-step explanation:
y = -2 ^x -1
<h2>Answer/Step-by-step explanation:</h2>
Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.
The ratio of between y-variable and x-variable would be constant.
Direct variation can be represented by the equation, , where k is a constant. Thus,
From the table given, it seems, as x increases, y also increases. Let's find out if there is a constant of proportionality (k).
Thus, ratio of y to x,
k = 0.5.
If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into , should give us the same constant if proportionality.
Let's check:
When x = 2, and y = 1:
,
,
When x = 3, y = 1.5:
,
When x = 5, y = 2.50:
,
The constant of proportionality is the same. Therefore, the relationship forms a direct variation.