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2 years ago

Which relation is a function

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

8 0

Answer:

Top left one on the attached, must be option A

Step-by-step explanation:

A function has to have unique input values and for each input value has to have an output value.

Analyzing the graphs we can see that only one of them is a function- top left one

All the others have repeat input values, therefore are not functions

All those points marked with red circle

<em>Refer to attached </em>

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For f(x)=4sin(x2) between x=0 and x=3, find the coordinates of all intercepts, critical points, and inflection points to two dec

telo118 [61]

Answer:

Intercepts:

x = 0, y = 0

x = 1.77, y = 0

x = 2.51, y = 0

Critical points:

x = 1.25, y = 4

x = 2.17 , y = -4

x = 2.8, y = 4

Inflection points:

x = 0.81, y = 2.44

x = 1.81, y = -0.54

x = 2.52, y = 0.27

Step-by-step explanation:

We can find the intercept by setting f(x) = 0

$4sin(x^2) = 0$

$sin(x^2) = 0$

$x^2 = n\pi$ where n = 0, 1, 2,3, 4, 5,...

$x = \sqrt(n\pi)$

Since we are restricting x between 0 and 3 we can stop at n = 2

So the function f(x) intercepts at y = 0 and x:

x = 0

x = 1.77

x = 2.51

The critical points occur at the first derivative = 0

$f^{'}(x) = 4cos(x^2)2x = 8xcos(x^2) = 0$

$xcos(x^2) = 0$

$x = 0$ or

$cos(x^2) = 0$

$x^2 = \frac{\pi}{2} + n\pi$ where n = 0, 1, 2, 3

$x = \sqrt{\pi(n+1/2)}$

Since we are restricting x between 0 and 3 we can stop at n = 2

So our critical points are at

x = 1.25, $y = f(1.25) = 4sin(1.25^2) = 4$

x = 2.17 , $y = f(2.17) = 4sin(2.17^2) = -4$

x = 2.8, $y = f(2.8) = 4sin(2.8^2) = 4$

For the inflection point, we can take the 2nd derivative and set it to 0

$f^[''}(x) = 8(cos(x^2) - xsin(x^2)2x) = 8cos(x^2) - 16x^2sin(x^2) = 0$

$cos(x^2) = 2x^2sin(x^2)$

$tan(x^2) = \frac{1}{2x^2}$

We can solve this numerically to get the inflection points are at

x = 0.81, $y = f(0.81) = 4sin(0.81^2) = 2.44$

x = 1.81, $y = f(1.81) = 4sin(1.81^2) = -0.54$

x = 2.52, $y = f(2.52) = 4sin(2.52^2) = 0.27$

3 0

3 years ago

Which mathematical expression means seven more than the product of three and x

vladimir2022 [97]

Answer:

More than means addition and product means multiplication. Therefore, seven more than the product of three and x would mean multiplying 3 and x together then adding 7 to that. Or, 3x + 7.

Step-by-step explanation:

7 0

3 years ago

o eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before add

Anna71 [15]

Answer:

Look at your answers for the last question in all four sets. Locate these four elements on the periodic table. Enter the name of the group that all four elements belong to. Watch your spelling! [Hint: If all four answers for the last question are not in the same group on the periodic table, redo your sets or contact your instructor.]

A screen reader friendly version of the periodic table (opens in a new window) is available, as well as a printable, black and white version (opens in a new window).

Step-by-step explanation:

7 0

2 years ago

If y varies directly as x , and y = 6 when x = 15, find y when x = 25 <br> .k = ______y = ______

viva [34]

At x = 25, y equals to 10.4.

6 0

3 years ago

Read 2 more answers

PLEASE HELP I WILL GIVE BRAINLIST PLEASE

ivolga24 [154]

Answer: D: 4.5

Step-by-step explanation:

So the Equation I used for this would be

6(2x+3) = 3(6x-3)

In Which the left is the Hexagon (The 6 is for the 6 Sides) and the right of the equation is the triangle (given the 3 for the 3 sides. In order to solve, we need to solve for x. Distribute the equation and your left with

12x+18=18x-9

-12x +9

27=6x

Divide to get X by itself

and your left with

4.5 = x

Hope it helped.

3 0

2 years ago

Which relation is a function​

Which relation is a function