Mathematics, 02.02.2020 21:55 leapfroggiez

Use the given graph to determine the limit, if it exists. a coordinate graph is shown with a horizontal line crossing the y axis at six that ends at the open point 2, 6, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3. find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..

Use the given graph to determine the limit, if it exists. a coordinate graph is shown with a horizon

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Answer from: wypozworski

The limit of the function does not exists.

Step-by-step explanation:

From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.

For x<2

f(x)=6

The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.

For x>2

f(x)=-3

The value of y is 1 at x=2, because of he close circles on (2,1).

For x=2

f(x)=1

Therefore the graph represents a piecewise function, which is defined as

$f(x)=\begin{cases}6& \text{ if } x2 \end{cases}$

The limit of a function exist at a point a if the left hand limit and right hand limit are equal.

$lim_{x\rightarrow a^-}f(x)=lim_{x\rightarrow a^+}f(x)$

The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.

$lim_{x\rightarrow 2^-}f(x)=6$

$lim_{x\rightarrow 2^+}f(x)=-3$

$6\neq-3$

Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.

Answer from: pennygillbert

As the graph moves from the left, over and over and over is consistently 6
when x = 1, limit is 6, 1.5, 6, 1.9, still 6, 1.999999999 still 6, 1.9999999999999999999999999 the limit is 6 still, now when x = 2, y = 1

but for the sake of a limit, it doesn't really matter if y = 6 or not at x = 2

as "x" is moving over and over and over from the left, the limit is consistenly, 6
now, it will not be 6 at x = 2, but that doesn't matter
the limit is "what is 'y' approaching as 'x' moves along", and is 6 from the left

now, from the right, is consistenly -3
same, as x = 2, y = 1 but
at x = 3, the limit is -3, x = 2.9, -3 still, 2.1, -3 still, 2.00000000000000000000000000000000001, the limit is still -3
thus, from the right, is -3

Answer from: Quest

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: