Two people start walking at the same time in the same direction. One person walks at 8 mph and the other person walks at 2 mph.
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Given functin is :
We know that the domain of the expression is all real numbers except where the expression is undefined. In given function, there is no real number that makes the expression undefined. Hence domain is all real numbers.
Domain: (-∞,∞)
Range is the set of y-values obtained by plugging values from domain so the range will also same.
Range: (-∞,∞)
If we increase value of x then y-value will also increase so that means it is an INCREASING function. You can also verify that from graph.
It crosses x and y-axes both at the origin
Hence x-intercept=0 and y-intercept=0
Graph is not symmetric about y-axis hence it can't be EVEN
Graph is not symmetric about origin so it is ODD.
There is no breaking point in the graph so that means it is a Continuous function.
There is no hoirzontal or vertical or slant line which seems to be appearing to touch the graph at infinity so there is NO asymptote.
END behaviour means how y-changes when x approaches infinity.
From graph we can see that when x-approaches -∞ then y also approaches ∞.
when x-approaches +∞ then y also approaches +∞.
Inequation 1:
to plot the pairs (x, y) for which the inequation holds, draw the line
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
draw the lines
i) use points (0, -3), (3, -1)
ii)
use points ( 0, 4), (3, 2)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
;
, not true so we color the region not containing this point
not true, so we color the region not containing the point (3, 3)
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.
to plot the pairs (x, y) for which the inequation holds, draw the line
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
draw the lines
i)
ii)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.