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1 year ago

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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