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2 years ago

The graph of which function is decreasing over the interval (–4, ∞)?

Mathematics

2 answers:

insens350 [35]2 years ago

7 0

This can be solved by the method of elimination.

We have been given that the function should decrease over (-4,∞)

So, since its between -4 and ∞ , we can eliminate option A and C. This is because options A and C are actually increasing over (-4,∞) and not decreasing.

So, this leaves us with options B and D. Next we find the vertex of the two functions. The vertex of Option B, that is $-(x+4)^2 +4$ lies at the point (-4,4) and decreases with x over the interval (-4,∞).

Whereas the option D, $-(x-4)^2+4$ has the vertex at (4,4) and hence the interval is not between -4 and infinite.

Hence Option B, $-(x+4)^2 +4$ is the answer asthe function is decreasing over the interval (–4, ∞)

padilas [110]2 years ago

3 0

I think second must b the answee

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Answer:

The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is 5 units to the right and 23 units down.

Explanation:

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The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

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This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

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The method is transforming the form of the function by completing squares:

Subtract 2 from both sides: g(x) - 2 = x² - 10x

Add the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25

Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²

Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0) was translated 5 units to the right and 23 units downward.

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