Which graph represents the function?
g(x) = {x if x < 2
{-3 if x >= 2

Which Graph Represents The Function?g(x) = {x If X &lt; 2 {-3 If X &gt;= 2

Answers

Answer 1

Step-by-step explanation:We have to graph the function g(x) which is given as:

g(x)=  x when x<2

and -3 when x ≥2.

Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.

Left hand limitat 2:

g(2-h)=lim h→0 2-h

       =2-0=2

Also right hand limit at x=2 is:

g(2+h)=lim h→0 (2+h)

         = 2+0=2

Also g(2)= -3.

As:

Left hand limit= Right hand limit but is not equal to function's value at that point.

Hence, the function is discontinuous at x=2.

so for x<2 we will get a graph of a line y=x.

and for x≥2 we will get a straight line y=-3 parallel to the domain.


Related Questions

if we have 765 toys and there are 3 people how many toys should we give to each man​

Answers

Answer:

255 is the answer

Step-by-step explanation:

Divide 765 by 3 and the answer will come .

Hope it will help u

help asap please ------------------

Answers

Answer:

Correct answer 1

Step-by-step explanation:

help pls!!

The functionſ is defined by f(x) = x(x + 3). If f(a) = 40 and a > 0, what is the value of a ?
A) 3
B) 5
C) 7
D) 8

Answers

Answer:

B) 5

Step-by-step explanation:

We are given the function:

[tex]f(x)=x(x+3)[/tex]

We are given that f(a) = 40 and a > 0 and we want to determine the value of a.

Substitute:

[tex]f(a)=40=a(a+3)[/tex]

Distribute:

[tex]a^2+3a=40[/tex]

Subtract 40 from both sides:

[tex]a^2+3a-40=0[/tex]

We can factor using 8 and -5. Hence:

[tex](a+8)(a-5)=0[/tex]

By the Zero Product Property:

[tex]a+8=0\text{ or } a-5=0[/tex]

Solve for each case:

[tex]\displaystyle a=-8\text{ or } a=5[/tex]

Since a > 0, we can eliminate the first solution. Hence:

[tex]a=5[/tex]

Our answer is B.

What is the inverse of the function f(x) = 2x - 10? A-. h(x) = 2x-5
B-. h(x) = 2x+5
C -. h(x) = 1/2x-5
D-. h(x) = 1/2x+5

need answer fast please​

Answers

Answer:

D

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = 2x - 10 ( add 10 to both sides )

y + 10 = 2x ( divide both sides by 2 )

[tex]\frac{y+10}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{2}[/tex] = [tex]\frac{1}{2}[/tex] x + 5 → D

3. Can a regular polygon have an interior angle of 160°​

Answers

the sum of interior angle is 180:

[tex]x + 160 = 180 \\ x = 180 - 160 \\ x = 20[/tex]

24 is 8 times as great as q

Answers

Answer:

Q = 3

Step-by-step explanation:

24 divided by 8 = 3
q = 3

If the measure of angle 5 is (3x + 50) degrees and the measure of angle 6 is (5x + 16) degrees, what value of x will guarantee equation AB \\ DE

Answers

Answer:

x = 17

Step-by-step explanation:

If AB // DE, then angle 5 and angle 6 are alternate interior angle and they should be congruent.

5x + 16 = 3x + 50

Subtract 16 from both sides

5x = 3x + 50 - 16

5x = 3x + 34

Subtract 3x from both sides

5x - 3x = 34

2x = 34

Divide both sides by 2

x = 34/2

x = 17

Answer:

To AB \\ DEangle 5 should be equal to angle 6

3x + 50 = 5x + 16

5x - 3x = 50-16

2x = 34

x = 17

Help me plz to find product

Answers

Step-by-step explanation:

Explanation is in the attachment

hope it is helpful to you ☺️

Is (2, 2) a solution of y <_ 4x – 6?
Choose 1 answer:
Yes or No

Answers

Answer:

Yes

Step-by-step explanation:

1. Looking at the question

The question states that...

[tex]x=2\\y=2[/tex]

2. Plugging it in

[tex]2\leq 4(2)-6\\2\leq 8-6\\2\leq 2[/tex]

Yes

Hope this helped! Please mark brianliest :)

Answer:yes

Step-by-step explanation:

Y<_4x-6

2<_4(2)-6

2<_8-6

2<_2

Amanda is playing her new video game, Track Runner. At first, she earned 20 points for winning a sprint. Then in the next race, she got – 25 points when she knocked over most of her hurdles. What is Amanda's total score now? To solve the problem, Amy added 20+( – 25) and came up with an answer of 5 points. Is Amy correct? Why or why not?

Answers

Answer: Amy is incorrect. The answer is -5 points.

Step-by-step explanation:

From the question, we are informed that Amanda earned 20 points for winning a sprint in the first race but got -25 points in the second race.

Based on the information above, Amanda's total score now will be:

= 20 + (-25)

= 20 - 25

= -5

The answer is -5 points.

Amy is wrong because (+) × (-) = (-)

(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.

(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.

Answers

Answer:

(a) [tex]x\³ - 6x - 6[/tex]

(b) Proved

Step-by-step explanation:

Given

[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root

Solving (a): The polynomial

A cubic function is represented as:

[tex]f = (a + b)^3[/tex]

Expand

[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]

Rewrite as:

[tex]f = a^3 + 3ab(a + b) + b^3[/tex]

The root is represented as:

[tex]r=a+b[/tex]

By comparison:

[tex]a = $\sqrt[3]{2}[/tex]

[tex]b = \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]

Expand

[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

Evaluate like terms

[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]

Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = 6 + 6r[/tex]

Equate to 0

[tex]f - 6 - 6r = 0[/tex]

Rewrite as:

[tex]f - 6r - 6 = 0[/tex]

Express as a cubic function

[tex]x^3 - 6x - 6 = 0[/tex]

Hence, the cubic polynomial is:

[tex]f(x) = x^3 - 6x - 6[/tex]

Solving (b): Prove that r is irrational

The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]

[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]

[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]

[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]

[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]

[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]

[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]

[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

An amount of 25,000 is borrow for 15 years at 5.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Answers

Answer: [tex]55,811.91[/tex]

Step-by-step explanation:

Given

Principal amount is 25,000

Time Period is [tex]t=15\ yr[/tex]

Rate of interest [tex]r=5.5\%[/tex]

Amount in compound interest is given by

[tex]\Rightarrow A=P\left(1+r\%\right)^t[/tex]

Insert the values

[tex]\Rightarrow A=25,000(1+\dfrac{5.5}{100})^{15}\\\\\Rightarrow A=25,000(1.055)^{15}\\\Rightarrow A=55,811.91[/tex]

Therefore, [tex]55,811.91[/tex] must be paid back

Get three real world examples of a rectangle prism

Answers

Answer:

a shipping container ,the ones they use in large cargo ships

A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).
Which equation represents the graphed function?

Answers

Answer:

y= (3/2)x-3

Step-by-step explanation:

We need two points to find the equation of a line. Let's take (2,0) and (4, 3).

In the equation y=mx+b, m represents the slope. To find the slope, we can calculate the change in y/change in x. For (2,0) and (4,3), the change in y is 3-0=3 and the change in x is 4-2=2. Therefore, our slope is 3/2.

Then, in the equation y=mx+b, we can plug 3/2 in for m to get y = (3/2)x+b. To find b, we can plug one point in, such as (2.0), to get 0=(3/2)(2) + b, 0=3+b, and b=-3, making our equation

y= (3/2)x-3

Answer:

the answer is C

Step-by-step explanation:

I NEED HELP ASAP!!!!!!!!!!!PLEASE

Answers

Answer:

74.8% approximately

Step-by-step explanation:

Area of circle is pi×r^2=pi×4^2=16pi=50.27 approximately

Area of pentagon (assumption regular pentagon)=5/2×apothem×side length=5/2(3.2)(4.7)=37.6

So the probability that it lands in the red is 37.6/50.27 approximately =74.8% approximately

HELP ME ASAP I need help with this problem

Answers

The answer is the second choice

B.

the solution is in the picture

What is the center of the circle:What is the center of the circle: (x+1)^2+(y-12)^2=25
1. 25
2. (1, -12)
3. 5
4. (-1, 12)

Answers

Answer:

option 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 1)² + (y - 12)² = 25 ← is in standard form

with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5


Write each as a percent. Use proportions.
7/25, 2/3, 3/8

Answers

Answer:

Step-by-step explanation:

[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]

Solve the equation and enter the value of x below. 4(x + 1) = 64 ​

Answers

Answer:

15

Step-by-step explanation:

Use the distributive property

4x+4=64, then subtract

4x=60, then divide

x=15

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

[tex]4(x + 1) = 64 \\ 4x + 4 = 64 \\ 4x = 64 - 4 \\ 4x = 60 \\ x = \frac{60}{4} \\ x = 15[/tex]

=> The answer is 15.

Which of the following values are in the range of the function graphed below?
Check all that apply.
O B. -1
O C. 5
D. 2
E. 1

Answers

Answer:

I believe the answer should be 0 to -1

Step-by-step explanation:

the range of a function is the lowest y value to the highest y value of that function. so in that example, the lowest y value you have on that curved line is at 0, and the highest y value you have on that curved line is 1, so the range should be from 0 to 1, or {0, 1}.

At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?

Answers

Answer:

$765

Step-by-step explanation:

[tex]interest \: = \frac{prt}{100} \\ = \frac{(450)(5)(14)}{100} \\ = 315 \\ total \: money \: = 315 + 450 \\ = 765[/tex]

A(n) = 450 + (n – 1)(0.05 • 450); $765.00

Solve the following equa
8 (2v + 8) = 96
оа
v = 2
ii need help

Answers

Answer:

1

Step-by-step explanation:

64+32 =96 that'd how I got the answer

Answer:

[tex]{ \tt{8(2v + 8) = 96}} \\ { \tt{2v + 8 = 12}} \\ { \tt{2v = 4}} \\ { \bf{v = 2}}[/tex]

HELP WILL GIVE BRAINLIEST

Answers

Answer:

6

Step-by-step explanation:

Follow 1 hour on the y axis to where it meets the line of best fit. In this case it is about 6 puzzles.

What is the equation of the
following line written in slope-Intercept form?

Answers

Answer:

y = -7x - 11

Step-by-step explanation:

Using the slot method calculate the probability that you would roll 3 sixes

Answers

Well you would roll 3 6’s if u rolled the dice and it landed on 3 and another 3 or 5 and a 1 and a 4 and a 2

1 2 3 4 5 6 7 8 9 10 Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y, of the rectangular garden that she creates if one side is x feet long

Answers

Answer:

[tex]Area = 60x - x^2[/tex]

Step-by-step explanation:

Given

[tex]Perimeter = 120[/tex]

[tex]Side\ 1 = x[/tex]

Required

The area of the garden

First, we calculate the length of the other side using:

[tex]Perimeter = 2 *(Side\ 1 + Side\ 2)[/tex]

This gives:

[tex]120 = 2 *(x + Side\ 2)[/tex]

Divide both sides by 2

[tex]60 = x + Side\ 2[/tex]

Make Side 2 the subject

[tex]Side\ 2 = 60 - x[/tex]

So, the area of the garden is:

[tex]Area = Side\ 1 * Side\ 2[/tex]

[tex]Area = x * (60 - x)[/tex]

Expand

[tex]Area = 60x - x^2[/tex]

I need help with 7 and 8 please

Answers

Answer:

Can't See 7 clearly

8) (9,9)

Step-by-step explanation:

[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]

Add x's and divide by 2

Add y's and divide by 2

Like taking the average of the coordinates.

The function shown is a composition of the functions g(x) and h(x) .

f(x)=2x√+8−7

Which of the following shows a possible decomposition of the function f(x) ?

Answers

what might be the following?

Which is the equation of a line parallel to the line with the equation: y = 14x + 2

y = -4x - 7

y = 4x + 2

y = 14x − 12

y = −14x + 3

Answers

Hi!

y = ax + b

y = 14x + 2 → a = 14 ∧ b = 2

Parallel lines have the same slope factor (a) so line parallel to the line with the equation y = 14x + 2 will be y = 14x - 12

This afternoon Zoe left school, rode the bus 11/12 of a mile, and then walked 1/12 of a mile to get home. How much farther did Zoe ride than walk?

Write your answer as a fraction or as a whole or mixed number.

Answers

Answer:

Zoe rode [tex]\frac{5}{6}[/tex] of a mile more than she walked.

Step-by-step explanation:

[tex]\frac{11}{12}-\frac{1}{12} =\frac{5}{6}[/tex]

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