Determine which is the graph of the given function.
2 answers:
Answer:
The graph of pairwise function is shown below.
Step-by-step explanation:
The given piece wise function is
It means for x<1, the function is defined as
At x=0,
At x=-1,
It means the graph passing through (0,5) and (-1,5.5). Joint these point to draw a line of x<1 and there is an open circle at x=1, because the the sign of inequality is <.
It means for x≥1, the function is defined as
At x=1,
At x=2,
It means the graph passing through (1,-3) and (2,-3.5). Joint these point to draw a line of x≥1 and there is an closed circle at x=1, because the the sign of inequality is ≥.
The graph of pairwise function is shown below.
Answer:
See attached picture and description below.
Step-by-step explanation:
Graph each equation as you would graph any linear function. Plot the y-intercept for the first equation at (0,5) then move down 0.5 units and to the right 1 unit. This is the right boundary and should be plotted with an open circle. (red graph.
The second equation should be graphed starting at the y-intercept (0,-2.5) then proceeding down 0.5 units and over 1 unit to the right. (blue graph)
See graph below for complete graph.
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Answer:
The graph is shown below.
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Explanation:
Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.
This is close to 5x-7, except we're off by 2 units.
In other words,
5x-7 = (5x-5)-2
since -7 = -5-2
Based on that, we can then say,
This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).
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Compare the equation to the form
We can see that
- a = -2
- h = 1
- k = 5
The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.
The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.
The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.
The graph is shown below. Some points of interest on the hyperbola are
- (-1,6)
- (0,7) .... y intercept
- (1.4, 0) .... x intercept
- (2, 3)
- (3, 4)
Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.
