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3 years ago

The function below has been transformed from f(x) = x2. Describe the transformation. h(x) = 4x2 + 12

Mathematics

1 answer:

Semenov [28]3 years ago

3 0

Answer:

vertically expanded by a factor of 4
then, translated upward 12 units

Step-by-step explanation:

If f(x) = x² and g(x) = 4x² = 4f(x), the function g(x) represents a vertical expansion of f(x) by a factor of 4.

If h(x) = g(x) +12, the function h(x) represents a translation of g(x) by 12 units upward.

Together, these transformations on f(x) are ...

vertical expansion by a factor of 4
translation upward by 12 units

_____

Please be aware that there are alternate transformations that will do the same thing:

h(x) = 4(f(x) +3) . . . . is a translation upward by 3, then a vertical expansion by a factor of 4

h(x) = f(2x) +12 . . . . is horizontal compression of f(x) by a factor of 2, then a translation upward by 12.

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Francesca wants to convert 1 meter to feet. Use what you know about customary measures to explain how she could do this.

Volgvan

Turn the feet into meters 1 meter = 100cm and if there is 12cms in a foot than divide 100cm by 12cm and you get 8.3ft

5 0

3 years ago

Help me with question a please ! With full workings !

frosja888 [35]

A)

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
Q&({{ 0}}\quad ,&{{ 2}})\quad 
% (c,d)
P&({{ 0.5}}\quad ,&{{ 0}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

$\bf QP=\sqrt{(0.5-0)^2+(0-2)^2}\implies QP=\sqrt{0.5^2+2^2}
\\\\\\
QP=\sqrt{\left( \frac{1}{2} \right)^2+4}\implies QP=\sqrt{ \frac{1^2}{2^2}+4}\implies QP=\sqrt{\frac{1}{4}+4}
\\\\\\
QP=\sqrt{\frac{17}{4}}\implies QP=\cfrac{\sqrt{17}}{\sqrt{4}}\implies QP=\cfrac{\sqrt{17}}{2}$

b)

since QR=QP, that means that QO is an angle bisector, and thus the segments it makes at the bottom of RO and OP, are also equal, thus RO=OP

thus, since the point P is 0.5 units away from the 0, point R is also 0.5 units away from 0 as well, however, is on the negative side, thus R (-0.5, 0)

c)

what's the equation of a line that passes through the points (-0.5, 0) and (0,2)?

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
Q&({{ 0}}\quad ,&{{ 2}})\quad 
% (c,d)
R&({{ -0.5}}\quad ,&{{ 0}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-2}{-0.5-0}\implies \cfrac{-2}{-0.5}$

$\bf m=\cfrac{\frac{-2}{1}}{-\frac{1}{2}}\implies \cfrac{-2}{1}\cdot \cfrac{2}{-1}\implies 4
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=4(x-0)\implies y=4x+2\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}$

7 0

3 years ago

What is x when y is 204?

STALIN [3.7K]

Answer:

x ,y = 204

Step-by-step explanation:

6 0

3 years ago

The slope of line XY is 1/8, and XY ⊥ AB

Ahat [919]

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}}
{\stackrel{slope}{\cfrac{1}{8}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{8}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{8}{1}}\implies -8}$

5 0

3 years ago

Jonathan plans to go to a carnival. The entrance is $3 and each ride cost 75 cents. Jonathan wants to spend no more than $20.

Mnenie [13.5K]

Answer:

22.6

Step-by-step explanation:

I assume you want to know how many rides he can do.

20$-3 = 17$

17÷.75 = 22.6 repeating

if you round up its about 23

4 0

3 years ago