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3 years ago

Find the domain of the function. (enter your answer using interval notation.) f(x) = 3x3 − 1 x2 + 2x − 15

Mathematics

1 answer:

Neporo4naja [7]3 years ago

6 0

Hello!

A cubic function is in the form of $f(x)=ax^{3}+bx^{2}+cx+d$ .

All cubic functions have a domain of all real numbers, the range also has a range of all real numbers.

Interval notation is used for representing a function/interval as a pair of numbers. Parentheses and brackets are used to show if the endpoints of a given function/interval are included or excluded. Brackets allow the endpoints to be included while parentheses exclude the endpoint.

Our first instinct would be that the domain is written as [-∞, ∞], but that is incorrect. Infinity is not a number, but it is a concept. This means that they are excluded from the domain.

Therefore, the domain of the function f(x) is (-∞, ∞).

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What does 1.75 represent in the second expression?

quester [9]

Answer:

Step-by-step explanation:

sana nakatulong mga lods

7 0

3 years ago

Which rule describes a composition of transformations that maps pre-image PQRS to image P"Q"R"S"?

FinnZ [79.3K]

The correct option is Option D $\boxed{{r_{y-axis}}o{R_{0,270^\circ }}\left({x,y}\right)}$ .

Further explanation:

A translation is a transformation that transforms the figure with a fixed distance in the same direction.

A rotation is the transformation that rotates the figure with given angles.

Given:

It is given that the two transformations that maps pre-image PQRS to image ${\text{P''Q''R''S''}}$ .

Step by step explanation:

Step 1:

It can be seen from the given figure that that the pre image is in the first quadrant and the image is the third quadrant.

The coordinates in the second quadrant represents as $\left({-x,y}\right)$ and in the third quadrant represents as $\left({-x,-y}\right)$ if $x,y$ are positive.

Therefore, the rotation is in the counter clockwise direction of $270^\circ$ .

Step 2:

The rotation of $270^\circ$ in the counter clockwise direction represents the coordinates as,

$\left({x,y}\right)\to\left({y,-x}\right)$

It can be seen that the coordinate of ${\text{PQRS}}$ are as follows,

$\begin{aligned}P=\left({1,1}\right)\hfill\\Q=\left(1,5}\right)\hfill\\R=\left({3,5}\right)\hfill\\S=\left({3,1}\right)\hfill\\\end{aligned}$

Then after rotation of $270^\circ$ counterclockwise on ${\text{PQRS}}$ $\left( {x,y}\right)\to\left({y,-x}\right)$ as,

$\begin{gathered}P\left({1,1}\right)\to\left({1,-1}\right)\hfill\\Q\left({1,5}\right)\to\left({5,1}\right)\hfill\\R\left({3,5}\right)\to\left({5,-3}\right)\hfill\\S\left({3,1}\right)\to\left({1,-3}\right)\hfill\\\end{gathered}$

Step 3:

Now apply the rule of $y$ axis of reflection ${R_{y-axis}}\left({x,y}\right)\to\left({-x,y}\right)$ on the above transformation as,

$\begin{gathered}\left({1,-1}\right)\to\left({-1,1}\right)=P''\hfill\\\left({5,1}\right)\to\left({-5,-1}\right)=Q''\hfill\\\left({5,-3}\right)\to\left({-5,-3}\right)=R''\hfill\\\left({1,-3}\right)\to\left({-1,-3}\right)=S''\hfill\\\end{gathered}$

Therefore, the given transformation is the rotation of $270^\circ$ counterclockwise followed by $y$ axis of reflection.

Therefore, this is the composition of transformation.

The composition of the given transformation can be written as,

${r_{y-axis}}o{R_{0,270^\circ}}\left({x,y}\right)$

Therefore, option D ${r_{y-axis}}o{R_{0,270^\circ}}\left({x,y}\right)$ is correct.

Learn more:

Learn more about what is the final transformation in the composition of transformations that maps pre-image abcd to image a"b'c"d"? a translation down and to the right a translation up and to the right a 270° rotation about point b' a 180° rotation about point b' brainly.com/question/2480946

Learn more about the transformation of function brainly.com/question/7297858

Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Transformations

Keywords: transformations, dilation, translation, rotation, counterclockwise, angle, clockwise, coordinates, mapping, rigid transformation, right side, left side, quadrant, composition.

3 0

3 years ago

Read 2 more answers

Read the following word problem, then choose which linear equation models the problem.

givi [52]

Answer:

Step-by-step explanation:

We know that length · width = area, width = w, and length = 2 * width = 2w so the answer is 2w · w = 338.

8 0

3 years ago

Assume that military aircraft use ejection seats designed for men weighing between 141.8 lb and 218 lb. If women's weights are

Mariulka [41]

Answer:

$P(141.8$

And we can find this probability with this difference and using the normal standard table:

$P(-0.639$

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(173.6,49.8)$

Where $\mu=173.6$ and $\sigma=49.8$

We are interested on this probability

$P(141.8$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(141.8$

And we can find this probability with this difference and using the normal standard table:

$P(-0.639$

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

8 0

3 years ago

The cost to rent a lawn tractor is $20 an hour plus the cost of gas.Shelly paid a total of $60 for gas in a lawn tractor she ren

pav-90 [236]

Answer:

Graph C

Step-by-step explanation:

It is graph C because it starts at $60 (the gas) and goes up $20 every hour (the hourly payment)

5 0

3 years ago