Find the domain and range of the relation and determine whether it is a function. y=x2-3

Answers

Answer 1

is that supposed to be x squared or 2x

Answer 2

A relation is a set of pairs, like {(2, 1), (5, 9), (3, 7)}

If the first coordinate is not repeated, like in this example, were we have only (2, 1) and not also (2, 8), for instance, then the relation is called a function.

A relation sometimes has too many pairs to be expressed by listing all of them. in such cases we use formulas which describe all the pairs.

We are given the relation is [tex]y=x^2-3[/tex]. This means that all pairs of this relation, are such that the second coordinate, is the first one squared, minus 3.

So each pair of this relation is : [tex](x, x^2-3)[/tex]

For any x, [tex]x^2-3[/tex] is only one value,

for example, if x=10, y can only be [tex]x^2-3=10^2-3=97[/tex]

We cannot possibly have both (10, 97) and (10, 16), for example, because the formula does not allow that.

this means 10 does not repeat as a first pair in this relation, and nor does any other value.

this makes the relation a function

The Domain is the set of all possible values x can be. Clearly, x can be any value, because no x makes [tex]x^2-3[/tex] undefined

Answer: The relation is a function, with Domain all real numbers

Related Questions

90 points correct answer

If the parent function f(x) = x2 is modified to g(x) = 2x2 + 1, which statement is true about g(x)?

It is an even function.

It is an odd function.

It is both an even and an odd function.

It is neither an even nor an odd function.

Answers

A is the answer
hope it helps

The answer is A because the function is even itself.

The sum of -4 and 8 times a number is multiplied by 3. The result is 15 less that 25 times the number. What is the number?

A) -12
B) 6/7
C) 0
D) 3
E) none of the above

Answers

3(-4 + 8x) = 25x - 15
-12 + 24x = 25x - 15
25x - 24x = -12 + 15
x = 3

answer is
D) 3

Find the value of x in the equation 2√ x
a. –5
b. 1
c. 16
d. 25 11. simplify the expression .
a.
b.
c.
d. + 20 = 15 + 3√ x

Answers

the answer to that question would be a c d

If the federal reserve decreases the reserve rate from 7% to 5%, how does this affect the amount of money that would result because of fraction-reserve rbanking from an initial deposit into a bank of $30,000

Answers

If the federal reserve rate was 7%, the money supply would be
30,000÷0.07=428,571

If the federal reserve rate was 5%, the money supply would be
30,000÷0.05=600,000

If the federal reserve decreases the reserve rate from 7% to 5%
600,000−428,571=171,429
The money supply increases by 171429

Hope it helps!

Final answer:

When the Federal Reserve decreases the reserve rate from 7% to 5%, the amount of money resulting from fraction-reserve banking increases. In this case, an initial deposit of $30,000 would result in $28,500 due to the change in reserve rate.

Explanation:

When the Federal Reserve decreases the reserve rate from 7% to 5%, it means that banks are required to hold a smaller percentage of deposits as reserves. This change allows banks to lend out a larger portion of the initial deposit. In this case, if the initial deposit into a bank is $30,000, the amount that would result from fraction-reserve banking would increase because the bank can now lend out a greater percentage of the deposit.

To calculate the new amount that would result from fraction-reserve banking, we need to calculate the reserve amount and the loan amount.

Calculate the reserve amount by multiplying the initial deposit ($30,000) by the new reserve rate (5%):

Reserve amount = $30,000 * 0.05 = $1,500

Calculate the loan amount by subtracting the reserve amount from the initial deposit:

Loan amount = $30,000 - $1,500 = $28,500

Therefore, the amount that would result from fraction-reserve banking from an initial deposit of $30,000 would be $28,500.

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How to solve equations

Answers

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand.

The distributive property is used mostly for simplifying parentheses in expressions/equations.

For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves.
The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.

6(x + 1) = 6x + 6

Which two expressions could be used to solve this problem?

Roberto ordered 4 pepperoni pizzas, 2 mushroom pizzas, and 3 cheese pizzas for his party. He paid the same price for each pizza. The total cost was $90. How much did each pizza cost?

Choose exactly two answers that are correct.

A.

4 × 2 × 3

B.

90 – 24

C.

90 ÷ 9

D.

90 obelus divided by(4 + 2 + 3)

Answers

I think the answer would most likely be C.

When is it necessary to use three points to name an angle? If CP bisects and DPB , what is the measure of angle CPB?

Answers

Angle CP = 45 degrees, because it's bisecting a right angle (90 degrees) and half of 90 degrees is 45.

Final answer:

In geometry, three points are used to name an angle when there are multiple angles that share the same vertex. If CP bisects angle DPB, angle CPB is divided into two equal angles, and the measure of angle CPB is half of the measure of angle DPB.

Explanation:

In geometry, it is necessary to use three points to name an angle when there are multiple angles that share the same vertex. By using three points, we can clearly identify which angle we are referring to. In this case, if CP bisects angle DPB, it means that angle CPB is divided into two equal angles, and CP is one of the dividing lines. Therefore, the measure of angle CPB is half of the measure of angle DPB.

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Including a 8 %8% sales tax, an inn charges $ 135$135 per night. Find the inn's nightly cost before the tax is added.

Answers

that would be $135 / 1.08 = $125

Find the value of x for which l is parallel to m. The diagram is not to scale.
a. 31
b. 62
c. 93
d. 149

Answers

If we continue the line which comes from line segment I till we reach line n then the angle formed will be 31 degrees ( interior alternate to 31 degrees)

x + 31 = 62 ( external angle of a triangle theorem).

Therfore x = 31 degrees answer

Summer paints a room that has 400 square feet of wall space in 2.5 hours. at this rate, how long will it take her to paint a room with 720 square feet of wall space?

Answers

400/2.5 = 160 sq feet every hour

720 sq ft/160 sq ft = 4.5 hours

Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of toms money to the amount of robs money was 4:7. Rob lost the latest competition, and now the ratio of the amount of robs money is 8:3. If rob had $280 before the last competition, how much rob have now that he lost the bet?

Answers

After Rob has lost, he will have 120 dollars.

before the bet Rob had 7 out of 11 ( 4+7)

280/7 = 40

after bet Rob had 3

3*40 = 120

he has $120

Kwamee bought kona beans that cost 11.00 and bought fuji beans that cost 7.50.he bought a total of 23 pounds of coffee and it cost 197.00 write a system of equations to solve how many pounds of kona and fuji beans kwamee bought

Answers

k= kona beans. f= fugi beans

k + f= 23. ==> -75k - 75f= -1725
11k + 7.5f= 197 ==> 110k + 75f= 1970

35k = 245
k= 7 lb of kona beans

7 + f = 23
f= 16 lb of fugi beans

The perimeter of a square garden is to be at least 20 ft but no more than 32 ft. find all possible values for the lengths of its sides using a compound inequality

Answers

20 < = 4a < = 32
20/4 < = (4/4)a < = 32/4
5 < = a < = 8

so the squares perimeter can be at least 5 ft but no more then 8 ft

Answer:

Answer in pic

Step-by-step explanation:

What is 19.2×108 minutes in hours? 1.152×1011 h 3.200×109 h 1.152×107 h 3.200×107 h

Answers

The answer to this question would be: 3.2 x 10^7 hours

To answer this question, you need to know how many minutes in an hour is, then convert the minutes into hours. To do this, you just need to divide the number with 60 minutes/hour. The calculation would be:

19.2×10^8 minutes / (60 minutes/hour) = 0.32 x 10^8= 3.2 x 10^7 hours

Could -2 be used as a base to rewrite 32? 64? Why or why not?

Answers

Since a base means that a value can be to the power of something to equal another number, we can try with -2. (-2)^1=-2, (-2)^2=4, (-2)^3=-8, (-2)^4=16, (-2)^5=-32, and (-2)^6=64. If a value (x) to the power of something (y) is equal to something (z), then x cannot be to the power of any number to equal -z unless x is -1. Therefore, since x=/ -1 in this case, -2 cannot be a base of 32 but it can be for 64

6=x+2/3

Please help ASAP!!! 10 Points!!! :)

Answers

x=18 you multiply 2/3 by its reciprocal 3/2 which cancels it and then multiply 6 by 3 which gives you 18

The answer is x= 16/3. I hope this helps love! :)

Which graph represents the system of inequalities?

Answers

I think it's C.
sorry if i'm wrong

an easy way is to test points
try (0,0), if it's true then the answer is C
it's false, not C

try (-4,5), if it's true, it's D
it's false, it's not D

try (1,4), if it's true, it's A
it's true

answer is A

What's the parabola in vertex for for (-5,0) and has a vertex (-2,1)

Answers

hello :
the parabola's equation is : f(x) = a(x+2)²+1

but ; f(-5) = 0
0 = a(- 5+2)²+1
9a+1=0.....a= -1/9
f(x) = (-1/9)(x+2)²+1

Is g(x)= 5 + 6/x a linear function

Answers

No. A linear function must be in the form f(x)= mx+b. Anytime you divide by x, the result when graphed is no longer linear. In fact, this is a reciprocal function.

What is the slope of the equation y = -x + 4

Answers

This is in slope-intercept form which is:

y = mx + b

In this equation, m is the slope, so the slope in this equation is -1

Hope this helps!

Find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $1500/semiannual period for 8 years at 2.5%/year compounded semiannually

Answers

The formula of the future value of an annuity ordinary is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT semiannual payment 1500
R interest rate 0.025
K compounded semiannual 2
N time 8 years
Fv=1,500×(((1+0.025÷2)^(2×8)
−1)÷(0.025÷2))
=26,386.75

Hope it helps!

How to find mass when given density and volume?

Answers

mass equals density times volume

If a(x)=3x+1 and b(x)=

Answers

b°a means that we plug a into the x value of b and go from there. In this case, we get [tex] \sqrt{(3x+1)-4} = \sqrt{3x-3} = \sqrt{3(x-1)} [/tex] (using the distributive property) and we have to figure out what the domain is. The domain is what x can equal, and since you can't have a square root of a negative number, 3(x-1) has to be greater than or equal to 0. Solving for that, we get 3(x-1)≥0. Dividing both sides by 3, we get x-1≥0. Next, we can add 1 to both sides to get x≥1. In interval notation, [1 encompasses 1 while (1 is everything above 1. In addition, it doesn't have to be less than anything, so we have ∞) at the end, making it [1, ∞). We have the parenthesis at the end because it doesn't include infinity, but everything less than it

The answer is C. [1, ∞] on edge

what hourly rate does the repair shop charge for labor?

Answers

its two hundred bucks

The mechanic's hourly rate is $55.

Understanding Labor Costs in a Repair Shop

To determine the hourly rate a repair shop charges for labor, we must analyze the information given and apply simple arithmetic operations. According to the examples provided, an auto mechanic charges a flat fee and an hourly rate for labor. For instance, a mechanic charging a flat fee of $75 per car, plus an hourly rate of $55 can be represented by the linear equation y = 75 + 55x, where 'y' is the total labor charge, and 'x' is the number of hours worked.

Example Calculation

Using the equation above, if the job takes 3.5 hours, the labor charge (y) would be calculated as $75 + ($55 imes 3.5) = $75 + $192.50 = $267.50. Hence, we can infer that the mechanic's hourly rate is $55.

The product of (a − b)(a − b) is a2 − b2.

Sometimes

Always

Never

Answers

Final answer:

The statement that the product of (a − b)(a − b) equals [tex]a^2 - b^2[/tex] is never true; the correct product is always [tex]a^2 - 2ab + b^2[/tex], representing the square of a difference formula.

Explanation:

The statement "The product of (a − b)(a − b) is [tex]a^2 - b^2[/tex]." is never true. Instead, using the distributive property to expand the expression (a − b)(a − b) yields a different result, as each term in the first binomial must be multiplied by each term in the second binomial.

The correct expansion is:

(a − b)(a − b) = a(a − b) - b(a − b)= aa - ab - ba + bb= [tex]a^2 - 2ab + b^2[/tex](since ab and ba are equivalent)

Thus, the product of (a − b)(a − b) is always [tex]a^2 - 2ab + b^2[/tex], which is the square of a difference formula, not [tex]a^2 - b^2[/tex] which is the difference of squares formula. The latter is applicable to the product (a + b)(a - b).

If f(x)=3/x+2-root x-3 complete the following statement (round answer to the nearest hundredth) f(7)=

Answers

hello :
f(x) = 3 /(x+2) - √(x-3)
f(7 ) = 3/(7+2) - √(7-3)
f(7) = 1/3 - √2 = 0.33 - 1.41 = - 1.1

Completely factor the expression.

w^2 - 15w + 54

Answers

It would be (w-6)(w-9) and so the solutions would be 6 and 9.

The equation 14m = 400.40 can be used to find the cost per yard m, in dollars, of mulch. what is the value of m? m = $

Answers

14m = 400.40
14m ÷14 = 400.40 ÷ 14
m = 28.60

Find the quotient.

110/10=

Answers

110/10
the / means divide
110 divided by 10 is 11.

The quotient is 11.

Hope this helps.

4.5/17 - x = 3/8 solve

Answers

First, you move the x to the other side by adding x on both sides, getting
4.5/17 = 3/8 + x.
Then, you subtract 3/8 from both sides, getting 4.5/17 + 3/8 = x, and then you simplify the fraction.
The final answer would be x = 87/136, or 0.64.

Answer:

The value of the equation is [tex]x=\frac{-15}{136}[/tex] Or [tex]x=-0.1102[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]\frac{4.5}{17}- x =\frac{3}{8}[/tex]

We need to solve the provided equation for x.

Add x to both side.

[tex]\frac{4.5}{17}- x+x=\frac{3}{8}+x[/tex]

[tex]\frac{4.5}{17}=\frac{3}{8}+x[/tex]

Subtract 3/8 from both sides.

[tex]\frac{4.5}{17}-\frac{3}{8}=x[/tex]

[tex]x=\frac{4.5}{17}-\frac{3}{8}[/tex]

[tex]x=\frac{36-51}{136}[/tex]

[tex]x=\frac{-15}{136}[/tex]

[tex]x=-0.1102[/tex]

Hence, the value of the equation is [tex]x=\frac{-15}{136}[/tex] Or [tex]x=-0.1102[/tex].

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