All categories

2 years ago

What are the domain and range of the function below?

Mathematics

1 answer:

Olin [163]2 years ago

5 0

Answer:

2nd answer option

Step-by-step explanation:

the domain is the interval or set of valid x values. the range is the same for valid y values.

so, what is the smallest x value we see in the functional graph ?

x = 0

there is no functional value for any x smaller than that.

and then the function goes on and on to the right in all eternity. that means it goes to infinity.

so, domain = [0, infinity)

please consider the round bracket at the end, because "infinity" is not a number.

now for the range and the y values.

in this case I start to ask for the largest y value.

y = 4

for no x value do we get a larger y value.

but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).

so, the range = (-infinity, 4]

"-infinity" is also not a number and therefore not included (hence the round bracket).

You might be interested in

50 point! Look at the picture attached. I will mark brainliest!

worty [1.4K]

Answer:

22°

Step-by-step explanation:

Triangle KJL ≅ Triangle MJL (RHS)

[JL = JL(common), KL = LM(given), angle KLJ = angle MLJ(given)]

we come up to the conclusion that 4x + 6 = 3x + 10

x = 4

∴angle KJL = 4(4) + 6 = 22°

6 0

3 years ago

Read 2 more answers

Nicole has a board 88 in.long.she needs to to cut it into filt a space 80 3/8 in long

Aleks [24]

Cut 7 and 6/8 in
Vhcmcghm

6 0

3 years ago

In this triangle, what is the value of X?

vovangra [49]

Answer:

The measure of angle x is $26.1\°$

Step-by-step explanation:

we know that

In the right triangle of the figure, the tangent of angle x is equal to divide the opposite side to angle x by the adjacent side to angle x

$tan(x)=\frac{26}{53}$

$x=arctan(\frac{26}{53})=26.1\°$

3 0

3 years ago

Solve y′′=sin(x) if y(0)=0 and y′(0)=5.<br><br> y(x)=?

Ksenya-84 [330]

Answer:

$y(x)=6x-sin(x)$

Step-by-step explanation:

Rewrite the differential equation as:

$\frac{d^{2} y }{dx^{2} } =sin(x)$

Integrate both sides with respect to x:

$\int\ \frac{d^{2} y }{dx^{2} } dx = \int\ sin(x) dx$

$\frac{dy}{dx} =-cos(x)+C_1$

Integrate one more time both sides with respect to x:

$\int\ \frac{dy}{dx} = \int\ -cos(x)+C_1 dx$

$y(x)=-sin(x)+C_1x+C_2$

Now that we find the solution, let's find its derivate:

$y'(x)=C_1-cos(x)$

Evaluating the initial conditions:

$y(0)=C_1(0)+C_2-sin(0)=0\\C_2=0$

$y'(0)=C_1-cos(0)=5\\C_1=5+1=6$

Replacing the value of the constants that we found in the differential equation solution:

$y(x)=6x-sin(x)$

6 0

3 years ago

1) The minimum thickness of Saturns A ring is one-tenth kilometer. Write this decimal using a negative exponent.

yulyashka [42]

Answer:

1) $10^{-1}$

2) $2^{-2}$

3) $12^{-2}$

Step-by-step explanation:

Using negative exponent rule:

1) one -tenth of kilometer =.1 = $\frac{1}{10}=10^{-1}$

Using negative exponent rule:

2) $\frac{1}{4} =\frac{1}{2^{2} }=2^{-2}$

Using negative exponent rule:

3) $\frac{1}{144} =\frac{1}{12^{2} }= 12^{-2}$

5 0

3 years ago