Frederick is making a graph that contains the ordered pairs (0, 3), (3, 2), (2, 1), and (0, 0). Will his graph represent a function? A. No, because it is not a straight line

B. Yes, because it will pass the horizontal line test

C. Yes, because it passes through the origin

D. No, because an x-value is repeated

An ordered pair may or may not represent a function.

The true statement is (d) No, because an x-value is repeated

The ordered pairs are given as:

For an ordered pair to be a function, no x-value must be repeated for different y-values.

From the given ordered pair, 0 is repeated for y-values 3 and 0.

This means that, the ordered pair is not a function.

Hence, the true statement is (d)

Read more about functions and relations at:

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That repeated x value is x = 0 due to the two points (0,3) and (0,0) being part of the same function. The input x = 0 maps to more than one output y = 3 and y = 0 at the same time. A function is only possible if any input x leads to exactly one output y. This is only if that x value is in the domain.

Visually, plotting (0,3) and (0,0) together shows that this graph does not pass the vertical line test. It is possible to draw a vertical line through more than one point on this graph. So this is a quick visual way to see that we don't have a function.

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: