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3 years ago

The graph of the cube root parent function y =∛ x is translated to form f(x) shown on the graph.

Mathematics

2 answers:

3241004551 [841]3 years ago

5 0

1. draw the graph of the parent function $y= \sqrt[3]{x}$ , as shown in the attached figure.

a few important point will be enough: (0, 0), (1, 1), (-1, -1), (8, 2), (-8, -2)

2. (0, 0) is an important point of the parent function, because as we go from the left to the right, the graph is concave up, than at (0, 0) it switches to concave down.

this point is called an inflection point, and in this function there is clearly only one.

3. The inflection point (0, 0) of the parent function has been translated to (-6, 1), so all points have been shifted 6 units left and one unit up

so $f(x)= \sqrt[3]{x+6}+1$

Answer: A

Remark, for horizontal shift, we use the opposite sign, for vertical shift, the same sign

Vlad1618 [11]3 years ago

5 0

Answer:

A. f(x)=∛x+6+1

Step-by-step explanation:

Just did it on edge!!

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1/3 x− 1/8 y=3 <br> 7y+9x=−2<br> please solve the system <br> 45 points for who does

photoshop1234 [79]

Answer:

$x=6\\y=-8$

Step-by-step explanation:

$\frac{1}{3}x-\frac{1}{8}y=3\\ 7y+9x=-2$

One method could be rewriting the second equation as x in terms of y and solving by replacing in the first equation.

$7y+9x=-2\\9x=-2-7y\\x=\frac{-7y-2}{9}$

Replace...

$\frac{1}{3}x-\frac{1}{8}y=3$

$\frac{1}{3}(\frac{-7y-2}{9})-\frac{1}{8}y=3$

$\frac{-7y-2}{27}-\frac{1}{8}y=3$

$-\frac{7}{27}y-\frac{2}{27}-\frac{1}{8}y=3$

add $\frac{2}{27}$ on both sides.

$-\frac{7}{27}y-\frac{1}{8}y=3+\frac{2}{27}$

Combine like terms

$\frac{(-7)(8)-(1)(27)}{(27)(8)} y=\frac{(3)(27)+2}{27}$

$\frac{-56-27}{216} y=\frac{81+2}{27}$

$\frac{-83}{216}y =\frac{83}{27}$

Now, to get rid of the fraction and isolate y, multiply by the reciprocal or the inverted fraction.

$(\frac{216}{-83}) \frac{-83}{216}y =\frac{83}{27}(\frac{216}{-83})$

$y=\frac{216}{-27}$

Simplify

$y=-8$

Now replace the value of y in either equation to find x.

$7y+9x=-2\\7(-8)+9x=-2\\-56+9x=-2$

add 56

$56-56+9x=-2+56\\9x=54\\$

Divide by 9

$\frac{9x}{9}=\frac{54}{9}\\ x=6$

To check whether these values are accurate, replace in either equation both values and you should have an equality. In this case I'll do it in both equations.

$\frac{1}{3}x-\frac{1}{8}y=3$

$\frac{1}{3}(6)-\frac{1}{8}(-8)=3$