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3 years ago

The black graph is the graph of y=f(x). Choose the equation for the red graph.

Mathematics

1 answer:

Makovka662 [10]3 years ago

6 0

Answer:

y-1 = f(x)

Step-by-step explanation:

Here, we want to choose the equation for the ref graph

The red graph as we can see is above the black

This means it is more positive

The difference between the two is just 1 unit

By the addition of 1 to the y-value of the black graph, we get the red

Thus, we have that;

y- 1 = f(x)

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Answer:

Volume of cylinder = 192π inch³

Step-by-step explanation:

Given:

Diameter of base = 8 inch

Length of cylinder = 12 inch

Find:

Volume of cylinder

Computation:

Radius of cylinder = Diameter of base / 2

Radius of cylinder = 8 / 2

Radius of cylinder = 4 inch

Volume of cylinder = πr²h

Volume of cylinder = π(4)²(12)

Volume of cylinder = π(16)(12)

Volume of cylinder = 192π inch³

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3 years ago

Rename 3 1/2 as the sum of 2 fractions

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Step-by-step explanation:

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Determine whether each of these functions from Z to Z is one-to-one. a) f(n) = n - 1 b) f(n) = n2 + 1 c) f(n) = nº d) f(n) = [n/

sesenic [268]

Answer: The correct option is

(a) f(n) = n - 1.

Step-by-step explanation: We are given to determine whether the given functions are one-to-one or not.

We know that a function y = f(x) is one-to-one if and only if

f(x) = f(y) ⇔ x = y.

That is, any two distinct elements cannot have the same image.

(a) The given function is

$f(n)=n-1.$

Let us consider that

$f(n_1)=f(n_2)\\\\\Rightarrow n_1-1=n_2-1\\\\\Rightarrow n_1=n_2.$

Similarly,

$n_1=n_2\\\\\Rightarrow n_1-1=n_2-1\\\\\Rightarrow f(n_1)=f(n_2).$

So, this function is one-to-one.

(b) The given function is

$f(n)=n^2+1.$

Let us consider that

$f(n_1)=f(n_2)\\\\\Rightarrow n_1^2+1=n_2^2+1\\\\\Rightarrow n_1^2=n_2^2\\\\\Rightarrow n_1=\pm n_2.$

That is, there may be two unequal elements having same image.

For example, f(-1)=(-1)²+1=1+1=2, f(1)=(1)²+1=1+1=2.

It implies that f(-1)=f(1) but 1 ≠ -1.

So, the given function is not one-to-one.

(c) The given function is

$f(n)=n^0.$

Here, the image of all the elements is 1.

For example, $f(2)=2^0=1,~~f(3)=3^0=1.$

f(2)=f(3) but 2≠3.

So, more than one element is having the same image and so the function cannot be one-to-one.

(d) The given function is

$f(n)=\left[\dfrac{n}{2}\right].$

Here, we see that

$f(2)=\left[\dfrac{2}{2}\right]=[1]=1,\\\\\\f(3)=\left[\dfrac{3}{2}\right]=[1.5]=1.$

So, f(2)=f(3) but 2≠3.

So, the given function is not one-to-one.

Thus, the correct option is (a).

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4 years ago