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4 years ago

What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

Mathematics

1 answer:

Darina [25.2K]4 years ago

4 0

Answer: First Option

−2 • f(x)

Step-by-step explanation:

The function $y=log_2(x)$ passes through point (2,1) since the exponential function $2 ^ x = 2$ when $x = 1$ .

Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair $(x_0, y_0)$ belonged to f(x), then $(x_0, -2y_0)$ belongs to the transformed function. Therefore, if $f(x) = log_2 (x)$ passed through point (2, 1) then the transformed function passes through point (2, -2)

The transformation that multiplies to f(x) by a factor of -2 is:

$y = -2 * f (x)$

and the transformed function is:

$y = -2log_2 (x)$

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Fran cut her sandwich into 6 pieces. If Fran ate 1/3 of her sandwich, how many pieces did he eat?

olga2289 [7]

2 pieces :)

Not sure if you wanted work but here is my explanation:

there are six pieces that she cut out, and she ate 1/3 of the six pieces,

1/3=2/6

since there are 6 pieces 1/3 would then equal 2 pieces. :)

Hope this helps:)

7 0

3 years ago

Read 2 more answers

Since 1851, exactly 119 hurricanes have hit Florida (this includes the years 1851 and 2019),—only direct hits by hurricanes are

alukav5142 [94]

Answer:

There is a 0.58% probability of Florida being struck by four or more hurricanes in the same year.

Step-by-step explanation:

Since we have only the mean during the interval, we can solve this problem using the Poisson probability distribution.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

Poisson probability distribution

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ is the mean in the given time interval.

In this problem, we have that:

Since 1851, exactly 119 hurricanes have hit Florida (this includes the years 1851 and 2019). Counting 1851 and 2019, there are 169 years in this interval. This means that $\mu = \frac{119}{169} = 0.704$

If the probability of hurricane strikes has remained the same since 1851, what is the probability of Florida being struck by four or more hurricanes in the same year?

This is $P(X \geq 4)$ .

Either Florida is struck by less than four hurricanes in a given year, or it is struck by 4 or more. The sum of these probabilities is decimal 1.

$P(X < 4) + P(X \geq 4) = 1$

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.704}*(0.704)^{0}}{(0)!} = 0.4946$

$P(X = 1) = \frac{e^{-0.704}*(0.704)^{1}}{(1)!} = 0.3482$

$P(X = 2) = \frac{e^{-0.704}*(0.704)^{2}}{(2)!} = 0.1226$

$P(X = 3) = \frac{e^{-0.704}*(0.704)^{3}}{(3)!} = 0.0288$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.4946 + 0.3482 + 0.1226 + 0.0288 = 0.9942$

Finally

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.9942 = 0.0058$

There is a 0.58% probability of Florida being struck by four or more hurricanes in the same year.

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3 years ago

Two word phrases for each expression t+32

mixas84 [53]

A number plus 32.
The sum of a number and 32.

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3 years ago

Perform (3x^3 – 2x^2 + 3x – 4) ÷ (x – 3) to find the value of the remainder.

BartSMP [9]

I believe the answers is B

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3 years ago

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The options for number two is

Blizzard [7]

The area of any quad = the base* height
for q 1:
the base=12 in
the height= 3 in
then the area = 12*3 = 36 sq in

for q 2:
the base= 14 in
the height = 4.5 in
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3 years ago