Which of the following function is graphed below?

Option A is the answer.

Step-by-step explanation:

Equations of the piecewise function is given as

y = x³ - 3

y = x² + 6

We have to find the domain of the sub-functions.

Since a dark point (2, 5) is lying on the graph that means equation is satisfied when we plug in the values of x and y.

y = x³ - 3

5 = 2³ - 3

5 = 8 - 3

5 = 5

y = x² + 6

5 = 2² + 6

5 = 4 + 6

5 = 10

which is not possible.

Therefore, this function represents the lower part of the graph.

y = x³ - 2  x ≤ 2

Now we put hollow point (2, 10) in both the equations,

10 = 2³ - 3

10 = 8 - 3

10 = 5

Again not possible.

y = x² + 6

10 = 2² + 6

10 = 4 + 6

10 = 10

Therefore, Upper portion of the graph is represented by the equation

y = x² + 6 x > 2

Option A is the answer.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation: