All categories

4 years ago

Write the equation of the function.

Mathematics

1 answer:

Hoochie [10]4 years ago

4 0

Answer:

f(x)=2sqrt( x + 3)

Step-by-step explanation:

We know it's a square root function because of the shape of the graph and it's moved to the left by 3 unit, so it has a d value of +3. We know it doesn't have a c value because it doesn't have a vertical translation as it's still at 0. For the a value, you can figure it out my substituting the graph points in and the values you know now then isolating and solving for the a value.

You might be interested in

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).

5 0

4 years ago

If the diameter of a circle is 8, then what is its area and its circumference?

Juli2301 [7.4K]

Answer:

A≈50.27

Diameter = 8

Using the formulas

A=πr2

d=2r

Solving forA

A=1

4πd2=1

4·π·82≈50.26548

4 0

3 years ago

Read 2 more answers

The side length of a square is:

Dominik [7]

Answer:

28x+20

Step-by-step explanation:

So the equation for perimeter is

Sx4 or S+S+S+S

So you would do

$4(7x+5)$

$28x+20$

4 0

3 years ago

Read 2 more answers

Find the area of a semicircle with a radius of 6 centimeters.

nlexa [21]

Answer:

Answer:

Measure of ∠y is 90°

Step-by-step explanation:

We see that,

∠x and ∠y are vertical angles and ∠x, 40°, 50° are in a straight line.

Since, we know, Sum of angles in straight line is 180°.

Then, ∠x + 40° + 50° = 180°

i.e. ∠x = 180° - 90°

i.e. ∠x = 90°

Also, we know, 'Vertical angles have equal measures'.

So, ∠y = ∠x = 90°

Hence, measure of ∠y is 90°

Read more on Brainly.com - brainly.com/question/9695253#readmore

Step-by-step explanation:

6 0

3 years ago

Write the point slope form of the line that passes through (-8,2) and is perpendicular to a line with a slope of -8

Fynjy0 [20]

Answer:

$y - 2 = \frac{1}{8}(x +8)$

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes. Since the slope of one line is -8, its perpendicular line will have the slope of 1/8.

Substitute m = 1/8 and (-8,2) into the point slope form of a line.

$y - y_1 = m(x-x_1)\\y - 2 = \frac{1}{8}(x --8)\\y - 2 = \frac{1}{8}(x +8)$

7 0

3 years ago