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2 years ago

What is f(x)=x^2 transformed 3 units to the left

Mathematics

1 answer:

stiv31 [10]2 years ago

7 0

Answer:

Equation:

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

Graph: see image

Step-by-step explanation:

Translation just means shift or slide. To show a LEFT shift in the equation, go in close to the x, inside the parenthesis with the x, for LEFT shift, insert +3.

Left and right shifts might be the opposite of what you may think. Minus a number shifts right and plus a number shifts left.

For the graph, see image. The answer is the green curve.

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Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.

Maru [420]

Answer:

$9\text{ln}|x|+2\sqrt{x}+x+C$

Step-by-step explanation:

We have been an integral $\int \frac{9+\sqrt{x}+x}{x}dx$ . We are asked to find the general solution for the given indefinite integral.

We can rewrite our given integral as:

$\int \frac{9}{x}+\frac{\sqrt{x}}{x}+\frac{x}{x}dx$

$\int \frac{9}{x}+\frac{1}{\sqrt{x}}+1dx$

Now, we will apply the sum rule of integrals as:

$\int \frac{9}{x}dx+\int \frac{1}{\sqrt{x}}dx+\int 1dx$

$9\int \frac{1}{x}dx+\int x^{-\frac{1}{2}}dx+\int 1dx$

Using common integral $\int \frac{1}{x}dx=\text{ln}|x|$ , we will get:

$9\text{ln}|x|+\int x^{-\frac{1}{2}}dx+\int 1dx$

Now, we will use power rule of integrals as:

$9\text{ln}|x|+\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+\int 1dx$

$9\text{ln}|x|+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+\int 1dx$

$9\text{ln}|x|+2x^{\frac{1}{2}}+\int 1dx$

$9\text{ln}|x|+2\sqrt{x}+\int 1dx$

We know that integral of a constant is equal to constant times x, so integral of 1 would be x.

$9\text{ln}|x|+2\sqrt{x}+x+C$

Therefore, our required integral would be $9\text{ln}|x|+2\sqrt{x}+x+C$ .

4 0

3 years ago

F(-3,-2), I(-4, 3), A(-2,3), M(1, -1)<br> to<br> I’(-4,-3), A’ (-2, -3), M’(1,1), F(-3,2)

icang [17]

I am not sure what exactly the question is, but all points are a reflection across the x-axis. I hope that helps.

8 0

3 years ago

How do i use systems of equations to eliminate two problems that are: -9x+2y=-24 and -x+2y=8

gulaghasi [49]

Eliinate y's
multiply top eqatyion by -1 and add to 2nd

9x-2y=24
<u>-x+2y=8 +</u>
8x+0y=32

8x=32
divid both sides b y8
x=4

sub back

-x+2y=8
-4+2y=8
add 4 to both sides
2y=12
divide both sides by 2
y=6
(x,y)
(4,6)

7 0

4 years ago

Please help with these questions thank youu!!

Masteriza [31]

$\\ \rm\Rrightarrow 2y=x-4$