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3 years ago

Which relation is a function?

Mathematics

2 answers:

Fed [463]3 years ago

7 0

Answer:

Bottom left graph

Step-by-step explanation:

Given are four graphs and we have to find out which is a function.

Any mapping from ordered pair x to y is a relation.

All relations need not be functions

A relation is a function only if the graph satisfies the vertical line test.

i.e. if we draw any vertical line in any point of the domain the line should cut the curve only at one point. Even if this is violated for one point, the relation is not a function

In the graph given, I one on top left has so many points on the vertical line. Hence not a function. II is a parabola open right and vertical line cuts atleast in two points one above and one below the x axis and not a funciton.

Bottom right most is a circle and any vertical line has two points of intersection above and below the x axis.

Bottom left is a graph since any vertical line cuts at only one point.

Answer is bottom left graph

Rzqust [24]3 years ago

6 0

The one in the bottoms left corner since no x values are repeated more than once

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e-lub [12.9K]

Answer:

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Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

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and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

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$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

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and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

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