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ahrayia [7]
1 year ago
14

Please help with this

Mathematics
1 answer:
Crazy boy [7]1 year ago
5 0

Answer:

  (a)  Horizontal line test

Step-by-step explanation:

A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.

<h3>Inverse relation</h3>

The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.

<h3>Inverse function</h3>

If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to <em>pass</em>.

A function will have an inverse function if it passes the Horizontal Line Test.

__

<em>Additional comment</em>

The attached graph shows a function (red curve) that <em>does not pass the horizontal line test</em>. Its inverse relation is the green curve, which you can see is <em>not a function</em>. It does not pass the vertical line test.

The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.

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Zinaida [17]

<u>We are given:</u>

The function: y = -16t² + 64

where y is the height from ground, t seconds after falling

<u>Part A:</u>

when the droplet would hit the ground, it's height from the ground will be 0

replacing that in the given function:

0 = -16t² + 64

16t² = 64                          [adding 16t² on both sides]

t² = 4                                [dividing both sides by 16]

t = 2 seconds                  [taking square root of both sides]

<u>Part B:</u>

for second droplet,

height from ground = 16 feet

time taken = t seconds

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initial velocity = 0 m/s

h = ut + (1/2)at²                 [second equation of motion]

16 = (0)(t) + (1/2)(10)(t²)

16 = 5t²

t² = 16/5

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4 0
3 years ago
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