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Anika [276]
3 years ago
7

Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x)=sqrt(x) and g

(x)=sqrt(0.5x)

Mathematics
2 answers:
SpyIntel [72]3 years ago
8 0
\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
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 \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{  B}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the y-axis}

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

with that template in mind, let's see    \bf f(x)=\sqrt{x}\qquad 
\begin{array}{llll}
g(x)=&\sqrt{0.5x}\\
&\quad \uparrow \\
&\quad  B
\end{array}

so B went form 1 on f(x), down to 0.5 or 1/2 on g(x)
B = 1/2, thus the graph is stretched by twice as much.
Alik [6]3 years ago
6 0
<h2>Answer:</h2>

The transformation of the function f(x) to g(x) is a horizontal stretch.

<h2>Step-by-step explanation:</h2>

The parent function f(x) is given by:

             f(x)=\sqrt{x}

and the transformed function g(x) is given by:

              g(x)=\sqrt{0.5x}

Now we know that the transformation of the type:

       f(x) → f(bx)

is a horizontal stretch if 0<b<1

and is a horizontal shrink if b>1

Here we have:

b=\dfrac{1}{2}=0.5

i.e.

0

This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.

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Which inequality represents the values of x that ensure triangle ABC exists? a triangle with side lengths of 6.5 units, 3.5 unit
nikdorinn [45]

Answer:

1 < x < 7.5

Step-by-step explanation:

This problem can be solved using given below property of triangle.

Sum of two sides is always greater than third side of triangle.

Difference of two sides is always lesser than third side of triangle.

_______________________________________________

Given

sides length

6.5 units

3.5 units

Third side is 2.5 +  x

using the property, Sum of two sides is always greater than third side of triangle.

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

using the property, Difference of two sides is always lesser than third side of triangle.

6.5 - 3.5 >  2.5 +x

=>3.5 >  2.5 +x

=> 2.5 +x  > 3.5

=> x  > 3.5 - 2.5

=> x  > 1

combining both we have

1 < x < 7.5

out of the given option none is 1 < x < 7.5

hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.

8 0
2 years ago
Read 2 more answers
One year Perry had the lowest ERA​ (earned-run average, mean number of runs yielded per nine innings​ pitched) of any male pitch
Blizzard [7]

Answer:

z score Perry z=-1.402

z score Alice z=-1.722

Alice had better year in comparison with Perry.

Step-by-step explanation:

Consider the provided information.

One year Perry had the lowest ERA​ of any male pitcher at his​ school, with an ERA of 3.02. For the​ males, the mean ERA was 4.206 and the standard deviation was 0.846.

To find z score use the formula.

z=\frac{x-\mu}{\sigma}

Here μ=4.206 and σ=0.846

z=\frac{3.02-4.206}{0.846}

z=\frac{-1.186}{0.846}

z=-1.402

Alice had the lowest ERA of any female pitcher at the school with an ERA of 3.16. For the​ females, the mean ERA was 4.519 and the standard deviation was 0.789.

Find the z score

where μ=4.519 and σ=0.789

z=\frac{3.16-4.519 }{0.789}

z=\frac{-1.359}{0.789}

z=-1.722

The Perry had an ERA with a z-score is –1.402. The Alice had an ERA with a z-score is –1.722.

It is clear that the z-score value for Perry is greater than the z-score value for Alice. This indicates that Alice had better year in comparison with Perry.

7 0
2 years ago
17/18 - 8/9 equal out to
Nutka1998 [239]
\frac{17}{18}-\frac{8}{9}=x
You must find a common denominator(bottom)
\frac{8}{9}×\frac{2}{2}=\frac{16}{18}
\frac{17}{18}-\frac{16}{18}=\frac{1}{18}
Your answer is x=\frac{1}{18}
8 0
3 years ago
Find ab if the coordinates of a are (3, 5 ( and b are (-3, -3)<br><br>a- 8<br>b- 6<br>c- 12<br>d- 10
strojnjashka [21]
If you use the distance formula you get 10.
6 0
2 years ago
Complete the following for a rectangular prism
denis-greek [22]

Width= 8 cm

Because 192 / 2 = 96 / 12 = 8

SA= (perimeter * height) + 2 (length * width)

SA= (20*12)+2(2*8)

SA= 240+32

SA= 272 cm2

6 0
3 years ago
Read 2 more answers
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