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mr_godi [17]
3 years ago
7

What transformation of the parent function, f(x) = x^2, is the function f(x) = -(x + 2) ^2

Mathematics
1 answer:
Alex777 [14]3 years ago
6 0

Answer:

f(x) reflects across the x-axis and translate left 2 ⇒ 2nd answer

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ f(x) = x²

∵ The parent function is f(x) = - (x + 2)²

- There is a negative out the bracket means we change f(x) to -f(x)

∴ f(x) is reflected across the x-axis

- The x is changed to x + 2, that means we translate the f(x) to the

  left two units

∵ x in f(x) is changed to (x + 2)

∴ f(x) is translated 2 units to the left

∴ f(x) reflects across the x-axis and translate left 2

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If you can, answer at least 2 question I put 10 points on it
igomit [66]

Answer:

a) one solution(x = 9)

b) no solution

c) infinite solutions

Step-by-step explanation:

a) To solve this equation, we can add 4 on both sides in order to isolate x:

x - 4 =5

+ 4     + 4

x = 9

Since x equals 9, that counts as only one solution, as there is only one value of x that makes the equation true.

b) We start by subtracting 2x from both sides to combine the variable terms:

2x - 6 = 2x + 5

-2x         -2x

-6 = 5

The statement, -6 = 5 is never true and it is not dependent on the value of x. This means there are no solutions to this equation.

c) We can start by subtracting 3x from both sides to combine the terms with x:

3x + 12 = 3x + 12

-3x          -3x

12 = 12

The statement above is always true, and no matter the value of x, it will always be true. This means there are infinite solutions to the equation.

8 0
3 years ago
A circle with a 2-inch radius is translated a distance of 12 inches perpendicular to the plane it is in. If copies of the circle
BartSMP [9]

Answer:

See below

Step-by-step explanation:

This will create a cylinder    volume = 1/2 pi  r^2 h = 1/2  pi  4  *  12

                                                            = 24 pi = 75.398 in^3

8 0
2 years ago
A drawer contain pens , 14 blue pens and 8 black pens , 14 silver paper clips , and 16 white paper clips . If you randomly selec
vichka [17]

Step-by-step explanation:

Total pens = 22

Total clips = 30

Probability of red pen = 0

Because there are no red pens

Probability of white clip = 16/30 = 8/15

4 0
3 years ago
In △ABC, m∠A=39°, a=11, and b=13. Find c to the nearest tenth.
Talja [164]

For this problem, we are going to use the <em>law of sines</em>, which states:

\dfrac{\sin{A}}{a} = \dfrac{\sin{B}}{b} = \dfrac{\sin{C}}{c}


In this case, we have an angle and two sides, and we are trying to look for the third side. First, we have to find the angle which corresponds with the second side, B. Then, we can find the third side. Using the law of sines, we can find:

\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{B}}{13}


We can use this to solve for B:

13 \cdot \dfrac{\sin{39^{\circ}}}{11} = \sin{B}

B = \sin^{-1}{\Big(13 \cdot \dfrac{\sin{39^{\circ}}}{11}\Big)} \approx 48.1


Now, we can find C:

C = 180^{\circ} - 48.1^{\circ} - 39^{\circ} = 92.9^{\circ}


Using this, we can find c:

\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{92.9^{\circ}}}{c}

c = \dfrac{11\sin{92.9^{\circ}}}{\sin{39^{\circ}}} \approx \boxed{17.5}


c is approximately 17.5.

8 0
3 years ago
Function g is a transformation of function f.
bulgar [2K]

The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given:

genera form of an exponential function is  y=aeᵇˣ

Now, equation for f(x) is

f(x) = e^{(log \;2)x} -2

Similarly, graph for g(x) is

g(x) = -3e^{(log \;2)x} +6

Comparing the two function a relation can  be establish

g(x) = -3[f(x)]

Learn more about Equation here:

brainly.com/question/2263981

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4 0
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