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creativ13 [48]
3 years ago
6

Giselle graphs the function f(x) = x^2. Robin graphs the function g(x) = –x^2. How does Robin’s graph relate to Giselle’s?

Mathematics
2 answers:
valentinak56 [21]3 years ago
6 0
I graphed the functions using 1,2,3 as the value of x.

My answer would be: <span>Robin’s graph is a reflection of Giselle’s graph over the x-axis.


</span>
Karolina [17]3 years ago
5 0

Robin's graph of the function g(x)=-x^2=-f(x) is the reflection of Giselle’s graph over the x-axis.

You can think in two ways:

1. For the function y=f(x), the sign minus before f(x) change the positive values of y into negative values. For example, f(2)=4 and g(2)=-4. This means that graphs of f(x) and g(x) are symmetric across the x-axis.

2. You can simply construct the table of values

\begin{array}{rcc}   x & f(x)=x^2 & g(x)=-x^2 \\   0 & 0 & 0 \\   1 & 1 & -1 \\   -1 & 1 & -1 \\   2 & 4 & -4 \\   -2 & 4 & -4 \\   3 & 9 & -9 \\  -3 & 9 & -9 \end{array}

and plot both graphs on the coordinate plane. From this diagram it is seen that graphs are symmetric over x-axis and Robin’s graph is a reflection of Giselle’s graph over the x-axis.

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We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find \\ \mu\;and\;\sigma.

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<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

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Having equations (1) and (2), we can form a system of two equations and two unknowns values:

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

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Rearranging these two equations:

\\ -0.6*\sigma = 100-\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:

\\ 0.6*\sigma = -100+\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

Summing both equations, we obtain the following equation:

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\\ 2.4*30 = 190-\mu (2)

\\ 2.4*30 - 190 = -\mu

\\ -2.4*30 + 190 = \mu

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