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4 years ago

9

(40 POINTS, WILL GIVE BRAINLIEST) There are 4 transformations for each function.

1 answer:

nika2105 [10]4 years ago

4 0

f(x) + n - translate the graph n units up

f(x) - n - translate the graph n units down

f(x + n) - translate the graph n units left

f(x - n) - translate the graph n units right

nf(x) - dilation of the graph along the Oy axis and the scale n

f(nx) - dilation of the graph along the Ox axis and the scale 1/n

-f(x) - symmetry of the graph with respect to the Ox axis

f(-x) - symmetry of the graph with respect to the Oy axis

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$f(x)=-3\cdot2^{x-1}-1\\\\g(x)=2^x\\\\3g(x)=3\cdot2^x-\text{dilatation by a scale of 3}\\\\-3g(x)=-3\cdot2^x-\text{symmetry of the graph with respect to the Ox axis}\\\\-3g(x-1)=-3\cdot2^{x-1}-\text{translate the graph 1 unit right}\\\\-3g(x-1)-1=f(x)=-3\cdot2^{x-1}-1-\text{translate the graph 1 unit down}$

$f(x)=-\dfrac{1}{4}\cdot2^{x+1}-1\\\\g(x)=2^x\\\\\dfrac{1}{4}g(x)=\dfrac{1}{4}\cdot2^x-\text{dilatation by a scale of}\ \dfrac{1}{4}\\\\-\dfrac{1}{4}g(x)=-\dfrac{1}{4}\cdot2^x-\text{symmetry of the graph with respect to the Ox axis}\\\\-\dfrac{1}{4}g(x+1)=-\dfrac{1}{4}\cdot2^{x+1}-\text{translate the graph 1 unit left}\\\\-\dfrac{1}{4}g(x+1)-1=f(x)=-\dfrac{1}{4}\cdot2^{x+1}-1-\text{translate the graph 1 unit down}$

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Assoli18 [71]

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3 years ago

How to find the equation of this line?

Bad White [126]

Answer:

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Step-by-step explanation:

The equation of a line in slope- intercept form is

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Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 4, 2 ) and (x₂, y₂ ) = (3, - 4) ← 2 points on the line

m = $\frac{-4-2}{3+4}$ = - $\frac{6}{7}$ , thus

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Using (- 4, 2 ), then

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4 years ago

Sally finds a coin with a radius of 1.5 centimeters and a thickness of 0.25 cm. It has a measured mass of 18.54 grams. How can S

mote1985 [20]

Answer:

Silver

Step-by-step explanation:

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<u>Volume of a cylinder</u>

$\textsf{V}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

Given:

r = 1.5 cm
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Substituting given values into the formula to find the volume:

$\sf \implies V=\pi (1.5)^2(0.25)$

$\sf \implies V=0.5625 \pi \:cm^3$

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<u>Density formula</u>

$\sf \rho=\dfrac{m}{V}$

where:

$\rho$ = density
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Given:

m = 18.54 g
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Substituting given values into the density formula:

$\implies \sf \rho=\dfrac{18.54}{0.5625 \pi}$

$\implies \sf \rho=10.49149385\:g\:cm^{-3}$

Given:

$\textsf{Density of Lead}=\sf 11.3\:g\:cm^{-3}$

$\textsf{Density of Silver}=\sf 10.49\:g\:cm^{-3}$

Therefore, as $\sf \rho=10.49\:g\:cm^{-3}$ the coin is made from silver.

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2 years ago

If the sphere shown above has a radius of 14 units then what is the approximate volume of the sphere

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Answer:

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Step-by-step explanation:

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Putting in the radius, we get:

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