10.02.2021

The table represents a function.
A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12.
Which value is an output of the function?

. 11

Faq

Mathematics
Step-by-step answer
P Answered by PhD

-2 is an output of the function.

Step-by-step explanation:

The given table is as follows:

\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right]

Here, the values written on the left side of table i.e. values of x are known as the domain values or input values to a function.

The values written on the right side of table i.e. values of f(x) are known as the range values or output values of the function f(x).

Let us consider the pairs of values:

(-6,8) then left side value is of x and right side value is of f(x)

i.e. when x=-6, the output value f(x) =8.

The same thing applies for all the pairs of values.

similarly for the pair (3,-2):

Left side value is of x and right side value is of f(x)

i.e. when x=3, the output value f(x) =-2.

So, the answer is:

-2 is an output of the function.

Mathematics
Step-by-step answer
P Answered by PhD

-2 is an output of the function.

Step-by-step explanation:

The given table is as follows:

\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right]

Here, the values written on the left side of table i.e. values of x are known as the domain values or input values to a function.

The values written on the right side of table i.e. values of f(x) are known as the range values or output values of the function f(x).

Let us consider the pairs of values:

(-6,8) then left side value is of x and right side value is of f(x)

i.e. when x=-6, the output value f(x) =8.

The same thing applies for all the pairs of values.

similarly for the pair (3,-2):

Left side value is of x and right side value is of f(x)

i.e. when x=3, the output value f(x) =-2.

So, the answer is:

-2 is an output of the function.

Mathematics
Step-by-step answer
P Answered by PhD

-2 is the output of the function.

Step-by-step explanation:

We have been given the table with two columns.

First column contains the values for x : -6, 7, 4, 3, -5

Second column contains the values for f(x):  8, 3, -5, -2, 12

The first column represents the imput values x which are independent. As the second value is labelled as f(x), it means all the values which we get after inputting values of x. Hence, f(x) represent the output values.

As the options given in the question for the values are -6,-2,4,7 , only one of these values match the outputs given in the second column which represents f(x),  and that value is -2

Mathematics
Step-by-step answer
P Answered by PhD

f(-6) = 8

f(3) = -2

f(x) = -5 when x is 4

Step-by-step explanation:

* Lets explain how to solve the problem

- The table of the function has two column

# First column labeled x with entries:

  -6 , 7 , 4 , 3 , -5

# Second column labeled f(x) with entries:

   8 , 3 , -5 , -2 , 12

∴ The ordered pairs of the function f(x) are:

  (-6 , 8) , (7 , 3) , (4 , -5) , (3 , -2) , (-5 , 12)

* Lets complete the missing

∵ The value of x in the first row is -6

∵ The value of f(x) in the first row is 8

∴ The function notation in the 1st row is f(-6) = 8

- The ordered pair given in the first row of the table can be

  written using function notation as f(-6) = 8

∵ The ordered pair whose x = 3 is (3 , -2)

∴ The value of f(x) when x = 3 is -2

∴ f(3) = -2

∵ The ordered pair whose f(x) = -5 is (4 , -5)

∴ The value of x when f(x) = -5 is 4

∴ f(x) = -5 when x is 4

Mathematics
Step-by-step answer
P Answered by PhD

The answer is C, The domain is a set of real numbers, and the range is y>0.

Step-by-step explanation:

If you recall from the instruction, the domain has to be whole numbers, because of it is not then the function will decrease into fractions never quite reaching zero. X has to be a real number, because it cannot be a fraction to keep an increasing rate, making the domain all real numbers. The range can never hit 0, so that means y>0.

Mathematics
Step-by-step answer
P Answered by PhD

The domain is {x : x ∈ R} , the range is {y : y > 0}

Step-by-step explanation:

* Lets explain how to solve the problem

- The general form of the continuous exponential function is

  y=a(e)^{kx} where a is the initial value and k is the growth factor

- We have some ordered pairs from the continuous exponential

  function

- The ordered pairs are:

  (0 , 4) , (1 , 5) , (2 , 6.25) , (3 , 7.8125)

- Lets substitute the values of x and y in the equation to find a , e^{k}

y=a(e)^{kx}

∵ x = 0 and y = 4 ⇒ 1st ordered pair

- Substitute x and y in the equation

4=a(e)^{k(0)}

4=a(e)^{0}

- The value of e^{0} = 1

∴ a = 4

- Substitute the value of a in the equation

y=4(e)^{kx}

∵ x = 1 and y = 5 ⇒ 1st ordered pair

- Substitute x and y in the equation

5=4(e)^{k(1)}

5=4(e)^{k}

- Divide both sides by 4

e^{k} = 1.25

- Substitute the value of e^{k} in the equation

y=4(1.25)^{x}

- The domain of the function is all the values of x which make the

  function defines

- The range is the values of y corresponding to x

∵ There is no value of x makes the function undefined

∴ The domain is all real numbers

∵ y never takes a negative value

∴ The range is all the real positive numbers

* The domain is {x : x ∈ R} , the range is {y : y > 0}

Mathematics
Step-by-step answer
P Answered by PhD

The domain is {x : x ∈ R} , the range is {y : y > 0}

Step-by-step explanation:

* Lets explain how to solve the problem

- The general form of the continuous exponential function is

  y=a(e)^{kx} where a is the initial value and k is the growth factor

- We have some ordered pairs from the continuous exponential

  function

- The ordered pairs are:

  (0 , 4) , (1 , 5) , (2 , 6.25) , (3 , 7.8125)

- Lets substitute the values of x and y in the equation to find a , e^{k}

y=a(e)^{kx}

∵ x = 0 and y = 4 ⇒ 1st ordered pair

- Substitute x and y in the equation

4=a(e)^{k(0)}

4=a(e)^{0}

- The value of e^{0} = 1

∴ a = 4

- Substitute the value of a in the equation

y=4(e)^{kx}

∵ x = 1 and y = 5 ⇒ 1st ordered pair

- Substitute x and y in the equation

5=4(e)^{k(1)}

5=4(e)^{k}

- Divide both sides by 4

e^{k} = 1.25

- Substitute the value of e^{k} in the equation

y=4(1.25)^{x}

- The domain of the function is all the values of x which make the

  function defines

- The range is the values of y corresponding to x

∵ There is no value of x makes the function undefined

∴ The domain is all real numbers

∵ y never takes a negative value

∴ The range is all the real positive numbers

* The domain is {x : x ∈ R} , the range is {y : y > 0}

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