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2 years ago

What transformations change the graph of f(x) to the graph of g(x)? f(x) = 3x2 g(x) = 9x2 - 4

Mathematics

2 answers:

myrzilka [38]2 years ago

3 0

For any function f(x) =y = f(x) + C ,c<0 the graph shifts down by c units.

For the function y = Cf(x) If C > 1 stretches it in the y-direction .We can stretch or compress it in the x-direction by multiplying x by a constant.

The given function f(x)= $3x^{2}.$ is stretched in y direction by 3 units and shifted down by 4 units to have the graph g(x)= $9x^{2}. -4.$

AURORKA [14]2 years ago

3 0

Multiply the whole equation by 3 then subtract 4 from te whole equation
vertically stretched by a factor of 3 and moved down 4 units is the translation

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tia_tia [17]

Answer:

$8-6i$

Step-by-step explanation:

Multiply out $(3-i)^2$ in order to find out which expression it is equivalent to.

1) Since the whole quantity is squared, write it out as $(3-i)(3-i)$ .

$(3-i)^2\\(3-i)(3-i)$

2) Multiply binomials by using the FOIL method. Multiply the terms that are listed first in each binomial, then the ones that are listed outermost when looking at both binomials, then innermost, and finally the last terms listed in each binomial. Simplify and combine like terms.

$(3-i)(3-i)\\9 - 3i - 3i + i^2$

$9 - 6i + i^2$

3) $i = \sqrt{-1}$ , so $i ^2$ must be $(\sqrt{-1} )(\sqrt{-1})$ . Thus, $i^2$ is equivalent to -1. Knowing this, simplify and combine like terms.

$9 - 6i + ((-\sqrt{1} )(\sqrt{-1} ))$

$9 - 6i -1\\8 - 6i$

Thus, it is equivalent to $8 - 6i$ .

6 0

3 years ago

If the standard deviation of a set of data is zero, what can you conclude about the set of values? The sum of the deviations fro

Rashid [163]

Answer:

All values are identical.

Step-by-step explanation:

We are given the following in the question:

If the standard deviation of a set of data is zero.

Then, all the values in data are identical.

This can be shown as:

Let all the terms in data be x.

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{nx}{n} = x$

Sum of squares of differences =

$\displaystyle\sum (x_i - x)^2 = 0$

$\sigma = \sqrt{\frac{0}{n}} = 0$

Thus, the correct answer is

All values are identical.

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