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3 years ago

What are the domain and range of the function? f(x) = ^3 square x - 3

Mathematics

1 answer:

DerKrebs [107]3 years ago

4 0

Step-by-step explanation:

$f(x) = \sqrt[3]{x - 3}$

The domain of a function are the values of $x$ that you can plug into the function $f(x)$ .

Values inside of a root must be non-negative, which means that $x - 3$ must be greater than or equal to zero. We can set up an equation to find the domain:

$x - 3 \geq 0$

$x \geq 3$

With this, we know the domain of the function is $[3, \inf)$ .

The range of a function are the values that $f(x)$ can have. Since the equation is a cube root, the value will always be non-negative, meaning the range of the function is $[0, \inf)$ .

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SOLVE THE QUESTION BELOW ASAP

qwelly [4]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) 16 feet

Part C) see the explanation

Step-by-step explanation:

Part A) Graph the function

Let

h(t) ----> the height in feet of the ball above the ground

t -----> the time in seconds

we have

$h(t)=-16t^{2}+98$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

To graph the parabola, find the vertex, the intercepts, and the axis of symmetry

<em>Find the vertex</em>

The function is written in vertex form

The vertex is the point (0,98)

Find the y-intercept

The y-intercept is the value of the function when the value of t is equal to zero

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98$

The y-intercept is the point (0,98)

Find the t-intercepts

The t-intercepts are the values of t when the value of the function is equal to zero

For h(t)=0

$-16t^{2}+98=0$

$t^{2}=\frac{98}{16}$

square root both sides

$t=\pm\frac{\sqrt{98}}{4}$

$t=\pm7\frac{\sqrt{2}}{4}$

therefore

The t-intercepts are

$(-7\frac{\sqrt{2}}{4},0), (7\frac{\sqrt{2}}{4},0)$

$(-2.475,0), (2.475,0)$

Find the axis of symmetry

The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

$x=0$ ----> the y-axis

To graph the parabola, plot the given points and connect them

we have

The vertex is the point $(0,98)$

The y-intercept is the point $(0,98)$

The t-intercepts are $(-2.475,0), (2.475,0)$

The axis of symmetry is the y-axis

The graph in the attached figure

Part B) How far is the artifact fallen from the time t=0 to time t=1

we know that

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98\ ft$

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

Find the difference

$98\ ft-82\ ft=16\ ft$

Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?

we know that

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

For t=2

$h(t)=-16(2)^{2}+98$

$h(2)=34\ ft$

Find the difference

$82\ ft-34\ ft=48\ ft$

The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1

therefore

The distance traveled from t=1 to t=2 is greater than the distance traveled from t=0 to t=1

8 0

2 years ago

How do i find y=1/2x+2 on a scatter plot <br>(Question 14)

Ainat [17]

Answer:

la cuestión is 15/7xt2

4 0

3 years ago

Of the 6 people attending a seminar, 3 have red hair.

marin [14]

Answer:

1/2

Step-by-step explanation:

Total -- 6 people

3 people -- 3/6 = 1/2

Therefore, the answer is 1/2

3 0

3 years ago

IF U HELP RN ILL GIVE U BRAINLIEST

shutvik [7]

Answer:

i need more info. that part dont help. if you took pic of the sentence they gv you that would be easier to work with.

Step-by-step explanation:

5 0

2 years ago

With a beginning balance of $2500 and no additional charges, there is no grace-period, you will just pay the minimum payment eac

valkas [14]

Answer:

a = $31.23 per month

b = $20.83 per month

c = 249.98 = $249.98 interest charges

= $624-249.98 = 374.02 profit part decrease 8% inc.

d = 35.35%

e = Answer is in the name; basic payment is a contract which means whilst account remains open charges are requested without fail. Should balance be less or on zero, charges are still applied.

Step-by-step explanation:

2500 x 1.2499 = interest only for start month 13 =3124.75

3124.75/ 100 x 1.08 = 8% of this = 249.98 each year.

We only have to divide each by 12 to work out monthly individual charges and subtract to find out payments.

3124.75 - 249.98 = 2874.77 = Total after charges each year.

249.98/12 = 20.83 = monthly charges.

3124.75- 2500 = 624.75 payments each year

624.75/12 = 52.06 month 1 payment before charge

52.06-20.83 =31.23 total minimum payment

2500 + 249.98

Percentage = 200:600 = 1/3 33% + (comparing to ratio 10:25 closer to 40%)

We find ratio 200:600= 33.33 + 49.995/24.75 = 2.02

33+2.02 = 35.35%

7 0

3 years ago