All categories

3 years ago

Which graph represents the function over the interval [−3,3] ? f(x)=⌈x+1⌉

Mathematics

1 answer:

CaHeK987 [17]3 years ago

4 0

Answer: The correct graph is the bottom left graph.

Step-by-step explanation:

Given function is f(x)=ceil(x+1)

To plot graph of f(x) in interval of(-3,3) :

ceil(x+1) is ceiling function

The output of ceil(x) is least integer greater than x

for example ceil(5.5)=6

For an interval of (-3,-2):

Take x=(-2.4)

x+1=(-1.4)

y=f(x)=ceil(x+1)=(-1)

Similarly,

For an interval of (-2,-1):

Take x=(-1.4)

x+1=(-0.4)

y=f(x)=ceil(x+1)=(0)

For an interval of (-1,0)

y=f(x)=1

For an interval of (0,1)

y=f(x)=2

For an interval of (1,2)

y=f(x)=3

For an interval of (2,3)

y=f(x)=4

Thus, The correct graph is the bottom left graph.

You might be interested in

F(x)=3x2+2x−3 <br><br> g(x)=2x+4

Yakvenalex [24]

Answer:

A: 6

B: 16

C: 2

D: -12

Step-by-step explanation:

They are asking you to multiply the equations:

(3x^2 + 2x - 3)(2x + 4)

Distribute and you should get:

6x^3 + 16x^2 + 2x - 12

The Coefficients A,B,C, and D are 6, 16, 2, and -12.

3 0

3 years ago

Give the equation of the line that passes through the points (4,6) and (-2,3)

Nutka1998 [239]

Answer:

y = 1/2x+4

Step-by-step explanation:

First we find the slope

m = (y2-y1)/(x2-x1)

= (3-6)/(-2-4)

= -3/-6

=1/2

The equation of a line in slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y =1/2x+b

Substitute one of the point into the equation

6 = 1/2(4) +b

6 = 2+b

b=4

y = 1/2x+4

3 0

3 years ago

Read 2 more answers

How many seconds will light leaving Los Angeles take to reach the following locations (a) San Francisco (about 500km), (b) Londo

kondor19780726 [428]

Answer:

a) It takes 0.0017s for the light to reach San Francisco.

b) It takes 0.033s for the light to reach London.

c) It takes 1.334s for the light to reach Mars.

d) It takes 149.7s for the light to reach Venus.

Step-by-step explanation:

Here we can solve this problem by using this following formula:

$s = \frac{d}{t}$

In which s is the speed(in km/s), d is the distance(in km) and t is the time(in s).

The light speed is 299 792 458 m / s = 299,792.458 km/s, so $s = 299,792.458$

(a) San Francisco (about 500km)

Find t when $d = 500$ . So

$s = \frac{d}{t}$

$299,792.458 = \frac{500}{t}$

$299,792.458t = 500$

$t = \frac{500}{299,792.458}$

$t = 0.0017s$

It takes 0.0017s for the light to reach San Francisco.

b) London(about 10,000km)

Find t when $d = 10,000$ . So

$s = \frac{d}{t}$

$299,792.458 = \frac{10,000}{t}$

$299,792.458t = 10,000$

$t = \frac{10,000}{299,792.458}$

$t = 0.033s$

It takes 0.033s for the light to reach London.

(c) the Moon (400,000km)

Find t when $d = 400,000$ . So

$s = \frac{d}{t}$

$299,792.458 = \frac{400,000}{t}$

$299,792.458t = 400,000$

$t = \frac{400,000}{299,792.458}$

$t = 1.334s$

It takes 1.334s for the light to reach Mars.

(d) Venus (0.3 A.U. from Earth at its closest approach).

Each A.U. has 149,59,7871 km.

So 0.3 A.U. = 0.3*(149,597,871) = 44,879,361.3. This means that $d = 44,879,361.3$ . So:

$s = \frac{d}{t}$

$299,792.458 = \frac{44,879,361.3}{t}$

$299,792.458t = 44,879,361.3$

$t = \frac{44,879,361.3}{299,792.458}$

$t = 149.7s$

It takes 149.7s for the light to reach Venus.

3 0

3 years ago

The sum of two numbers is 28. one number is 14 more. find the numbers

ruslelena [56]

The numbers are: "7 " and "21 " .
_______________________________________
Explanation:
_______________________________________
The numbers are: "x" and "x + 14" .

x + (x + 14) = 28 . Solve for "x" ; and then solve for "x + 14" .
_______________________________________
→ x + (x + 14) = 28 ;

Rewrite as:

→ x + x + 14 = 28 ;

→ 1x + 1x + 14 = 28 ;

→ 2x + 14 = 28 ;

Subtract "14" from each side of the equation;

→ 2x + 14 − 14 = 28 <span>− 14 ;

</span> → 2x = 14 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 2x / 2 = 14 / 2 ;

→ x = 7 .
_________________________________________
So; one of the numbers is: " 7 " .

The other number is: " x + 14 " ; which equals: " 7 + 14 = 21".

The other number is: "21 " .
_________________________________________
The numbers are: "7 " and "21 " .
_________________________________________

5 0

3 years ago

PLEASE HELP WILL GIVE BRAINLIEST Which of the following scale factors will result in an enlargement? A. k < –1 B. –1 < k &

Sergio [31]

Answer: OPTION A.

Step-by-step explanation:

By definition, a dilation can be an enlargement or a reduction of the shape.

An enlargement is when dilation creates a larger image and a reduction is when dilation creates a smaller image.

When, the scale factor is greater than 1, the image is an enlargement and when the scale factor is between 0 and 1, the image is a reduction.

It is important to know that with a negative scale factor the enlargement will will be inverted and it will also be on the other side of the center of dilation.

Knowing this, we can say that the scale factor that will result in an enlargement is:

$k$

5 0

3 years ago