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Describe the translation of the function from the parent function f(x) = x².

kkurt [141]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\

\end{array}\\$

$\bf \begin{array}{llll}
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}
$

now, notice the template above... now let's see your function $\bf y=x^2+4\implies 
\begin{array}{llllll}
y=&1(&1x&+&0)^2+&4\\
&A&B&&C&D
\end{array}$

so.. what do you think was the shift then?

8 0

2 years ago

A dictionary contains the following 9 words: two, mice, three, squeaking, the, blind, deaf, birds, rabbits. What is the probabil

IgorC [24]

Answer:

The correct answer is B. 1/729

Step-by-step explanation:

1. Probability of any of the nine words would be randomly cited.

Using the Laplace Rule, we calculate that probability is 1/9

2. Now let's calculate the probability of any two - word phrase in specific order from those nine in the dictionary. We should remember that the probability of occurrence of two or more statistically independent events is equal to the product of their individual probabilities. So,

1/9 * 1/9 = 1/81

3. Using the same Multiplication Rule, we can calculate the probability of a random generation of the phrase "three blind mice", in that specific order. Because there are other phrases that could be generated with those three words, but in different order. The question was specific about the order.

1/9 * 1/9 * 1/9 = 1/729

The probability of randomly generating the phrase "three blind mice" is 1/729 or 0.137%

7 0

2 years ago

9n - 8d (n = 3 and d = 2

leva [86]

Answer:

11

Step-by-step explanation:

9(3)-8(2)

27-16

11

3 0

2 years ago

Eloise started to solve a radical equation in this way: Square root of negative 2x plus 1 − 3 = x Square root of negative 2x plu

andreyandreev [35.5K]

Here I copy the steps and indicate where the error is.

Square root of negative 2x plus 1 − 3 = x=> this is the starting equation

√[ - 2x + 1] - 3 = x

Square root of negative 2x plus 1 − 3 + 3 = x + 3 in this step she added 3 to each side, which is fine

Square root of negative 2x plus 1 = x + 3 she made the addtions => fine

Square root of negative 2x plus 1 − 1 = x + 3 – 1 due to plus 1 in inside the square root, this step will not help

Square root of negative 2 x = x + 2 wrong! she cannot simplify - 1 that is out of the square root with +1 that is inside the square root

Then, from here on all is wrong, but she made other additional mistakes.

(Square root of negative 2 x)2 = (x − 4)2 −2x the right side should be (x+2)^2 which is x^2 + 4x +4 not (x-4)^2 - 2x

Later she made a mistake changing the sign of -8x to +8x

Those are the mistakes. Finally, the global error is that she should verify whether the found values satisfied the original equation.

3 0

2 years ago

Read 2 more answers

A negative exponent means repeated_________?

allsm [11]

negative exponent means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125. Or many divides: Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008.

hope it helps

6 0

3 years ago