Which of the following are characteristics of the graph of the square root
parent function? Check all that apply.
A. It has a domain of x 0.
B. It has a range of yz 0.
O c. It starts at the origin.
D. It is a straight line.

Choices A and B have typos in them, so its not clear what you're trying to say for those parts. However, the domain of is meaning that x can be 0 or larger. In other words, we can't have x be negative. Similarly, y is the same story because has the inverse , but only when , so therefore as well. In short you can say both x and y are nonnegative.

To summarize so far, the domain is and the range is

Since x = 0 and y = 0 are the smallest x and y values possible, this means (x,y) = (0,0) is the left-most point or where the graph starts. This is the origin. Choice C is a true statement.

Choice D on the other hand is not a true statement. Graph out and you'll see that a straight line does not form, but instead a nonlinear curve that grows forever. That growth gradually diminishes as x gets larger. Algebraically you can pick three points from the function and show that the slopes are different. Say the three points are P, Q and R. If you can show that slope of PQ does not equal slope of QR, then the function is not linear.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

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: