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DedPeter [7]
3 years ago
8

Use graphing technology to find the range of the function f(x)=x2 +6x+9

Mathematics
1 answer:
lbvjy [14]3 years ago
5 0

Answer:

See below.

Step-by-step explanation:

Refer to the graph.

The range of a graph is the span of y-values it covers.

From the graph, we can see that the span of y-values is all values greater than or equal to 0.

Therefore, our range is, in interval notation:

[0,\infty)

Note that we use brackets with the 0 because 0 is included in our range.

In set notation, this is:

\{y|y\in\mathbb{R},y\geq 0\}

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Solve for x, 0 ≤ x ≤2π (2cosx-1)(2sinx+√3 ) = 0
vladimir1956 [14]

Answer:

x = π/3, x = 5π/3, x = 4π/3

Step-by-step explanation:

Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3  = 0.

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Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.

Similarly:

\:2\sin \left(x\right)+\sqrt{3}=0,\\2\sin \left(x\right)=-\sqrt{3},\\\sin \left(x\right)=-\frac{\sqrt{3}}{2}

The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.

So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.

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3 years ago
Lhbui=]\k;m#wqeryuk;'][4<br>\75'];[pouy64awreygukpl[;'k;yftawe<br>Q$\
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Hmmm not sure I can answer that but if you do ever have a question let me know! :)

Step-by-step explanation:

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