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Ivan
3 years ago
13

Write a function rule for the table. x ƒ(x) 3 –1 4 0 5 1 6 2

Mathematics
1 answer:
MaRussiya [10]3 years ago
3 0

Answer:

Step-by-step explanation:

When one variable depends on another variable according to a rule it is known as function:

For example if you want an output of 2 and the input value is 4. Then you will subtract 4 from x

We have to find x f(x).

x f(x) =?

f(x) = x-4

Now input value is:  x= 3

x f(x)

3 (x-4)

3 (3-4)

3 -1

Now x= 4

x f(x)

4 (x-4)

4 (4-4)

4 0

Now x=5

x f(x)

5 (x-4)

5 (5-4)

5 1

Now x=6

x f(x)

6 (x-4)

6 (6-4)

6 2 ....

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Graph the following three equations on your own device and answer the questions below.
Alina [70]

Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.

<h3>What are the characteristics of each of the three functions?</h3>

a) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(10) = 5 · 10 + 7

f(10) = 57

Case 2

f(10) = 10² + 6

f(10) = 106

Case 3

f(10) = 2¹⁰ + 3

f(10) = 1027

b) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(100) = 5 · 100 + 7

f(100) = 507

Case 2

f(100) = 100² + 6

f(100) = 10006

Case 3

f(100) = 2¹⁰⁰ + 3

f(100) = 1.267 × 10³⁰ + 3

c) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(1000) = 5 · 1000 + 7

f(1000) = 5007

Case 2

f(1000) = 1000² + 6

f(1000) = 1000006

Case 3

f(1000) = 2¹⁰⁰⁰ + 3

f(1000) = (1.268 × 10³⁰)¹⁰ + 3

f(1000) = 10.744 × 10³⁰⁰ + 3

f(1000) = 1.074 × 10³⁰¹ + 3

e) The <em>third</em> function increases the fastest.

f) In this part we need to compare the <em>third</em> function with respect to the <em>first</em> and <em>second</em> functions:

5 · x + 7 = 2ˣ + 3

2ˣ - 5 · x   = 4

The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other <em>first</em> function at x = 4.81.

x² + 6 = 2ˣ + 3

2ˣ - x² = 3

The solution of the equation is x = 4.588. The function will exceed the other <em>second</em> function at x = 4.588.

g) Yes, <em>exponential</em> functions with bases greater than 1 will surpass <em>polynomic</em> function at any point x such that x > 0.

h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:

Case 1

Domain - All <em>real</em> numbers.

Range - All <em>real</em> numbers

Case 2

Domain - All <em>real</em> numbers.

Range - [6, +∞)

Case 3

Domain - All <em>real</em> numbers.

Range - (3, +∞)

To learn more on functions: brainly.com/question/12431044

#SPJ1

5 0
1 year ago
I need help with this pleaseee!
ololo11 [35]
Probably B

STEP BY STEP
7 0
3 years ago
Find the inequality represented by the line. Need help immediately. Explain if you can
Debora [2.8K]

Answer:

ok fine 1.3x+4y<10

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Find the value of each variable so that the quadrilateral is a parallelogram.
Dmitry [639]

Answer:

<em>x = -2</em>

<em>y = -5</em>

Step-by-step explanation:

<u>Properties of a Parallelogram</u>

  • Two pairs of opposite sides are parallel.
  • Two pairs of opposite sides are equal in length.
  • Two pairs of opposite angles are equal in measure
  • The diagonals bisect each other.
  • Adjacent angles are supplementary.
  • Each diagonal divides the quadrilateral into two congruent triangles.

Each diagonal is divided into two measures expressed with variables. Since diagonals bisect each other:

y + 23 = -4y - 2.  And

-2x + 6 = x + 12

Solve the first equation. Adding 4y:

5y + 23 = - 2

Subtracting 23:

5y = -25

Dividing by 5:

y = -5

Solve the second equation. Subtracting x and 6:

-3x = 6

Dividing by -3:

x = -2

Solution:

x = -2

y = -5

4 0
3 years ago
I'd the ratio 25 to 16 proportional to the ratio 5 to 4 explain
Arturiano [62]
Yes, 5:4 is the simplified form of 25:16. 25 divided by 5 is 5 (the lowest possible number it can be made into). 16 divided by 4 is 4 (also the lowest possible number it can be made into). 
4 0
3 years ago
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