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chubhunter [2.5K]

2 years ago

10

The parent function f(x)=log^3x has been transformed by reflecting it over the X axis, stretching it vertically by a factor of t

wo and shifting it up three units. Which function is representative of this transformation

1 answer:

NARA [144]2 years ago

6 0

Answer:

b

Step-by-step explanation:

You might be interested in

Given f(x)=4x+5 and g(x)= x^2+x; find (f∘g)(-5)<br> Please show all steps thank you

Greeley [361]

Answer:

$(f\circ g)(-5)=85$

Step-by-step explanation:

We are given:

$\displaystyle f(x)=4x+5\text{ and } g(x)=x^2+x$

And we want to find:

$(f\circ g)(-5)$

This is equivalent to:

$\displaystyle =f(g(-5))$

So, we will evaluate g(-5) first, which yields:

$\displaystyle g(-5)=(-5)^2+(-5)=25-5=20$

So:

$=f(g(-5))=f(20)$

Then:

$\displaystyle f(20)=4(20)+5=80+5=85$

Therefore:

$(f\circ g)(-5)=85$

6 0

3 years ago

3 more than 6 times a number

Snowcat [4.5K]

Answer:

assuming you're looking for an expression, it would be written as "6x+3".

4 0

2 years ago

Read 2 more answers

The toy shop is located at (-2, 3) and the ice skating rink is located at (-2, -5). Plot these points on the coordinate grid. If

natta225 [31]

Answer:

8 miles

Step-by-step explanation:

We start by calculating the distance between the two points

To calculate this, we use the distance formula

Let the distance be D

We have the formula as;

D = √(x2-x1)^2 + (y2-y1)^2

D = √(-2+2)^2 + (-5-3)^2

D = √(64)

D = 8 units

Since 1 unit is 1 mile,

then 8 units will be 8 * 1 = 8 miles

7 0

2 years ago

When you divide a whole number by a fraction with a numerator of 1, explain how you can find the quotient?

Kryger [21]

You take the whole number and put it in a fraction over 1 then divide by flipping the second fraction and multiplying

4 0

2 years ago

Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the

sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let $y(t)$ be the depth of water in the barrel at time $t$ , where $y$ is measured in inches and $t$ in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

$\frac{dy}{dt}=-k\sqrt{y}$

where $k$ is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by $\frac{1}{\sqrt{y}}$

$\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k$

Multiply by $dt$

$\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt$

Take integral

$\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt$

Integrate

$2\sqrt{y}=-kt+C$

Isolate $y$

$y(t)=(\frac{C}{2} -\frac{k}{2}t)^2$

We know that the water level starts at 36, this means $y(0)=36$ . We use this information to find the value of $C$ .

$36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12$

$y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2$

At t = 1, y = 34

$34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}$

So our formula for the depth of water in the barrel is

$y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\$

To find the time, $t$ , at which all the water leaks out of the barrel, we solve the equation

$\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49$

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

5 0

3 years ago