# Complete the table of values and plot the transformed points to obtain thegraph of y=-2(-1/3(x+2))^2-4Table with four columns: y = f(x) | y = f(– 1/3 x) | y = –2f(– 1/3 x) | y = –2f(–...

Complete the table of values and plot the transformed points to obtain the
graph of y=-2(-1/3(x+2))^2-4

Table with four columns:

y = f(x) | y = f(– 1/3 x) | y = –2f(– 1/3 x) | y = –2f(– 1/3 (x + 2))^2 – 4
|                     |                          |
(0, 0)    |                     |                          |
(1, 1)    |                     |                          |
(2, 4)    |                     |                          |
(3, 9)    |                     |                          |

sciencesolve | Teacher | (Level 3) Educator Emeritus

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Since the set of ordered pairs of the function f(x)=y is {(0, 0);(1, 1);(2, 4);(3, 9)}=>f(x)=y=x^2

You need to find the coordinate y if f(-1/3x) = (-1/3x)^2 = 1/9x^2

Since x is at denominator, it needs to be != 0.

If x = 1 => f(-1/3x) = 1/9

If x = 2 => f(-1/3x) = 1/36

If x = 3 => f(-1/3x) = 1/81

The graph of the function f(-1/3x) =1/9x^2  is:

If y = -2f(-1/3x) = -2/9x^2

If x = 1 => -2f(-1/3x) = -2/9

If x = 2 => -2f(-1/3x) = -2/36

If x = 3 => -2f(-1/3x) = -2/81

The graph of the function f(-1/3x) =-2/9x^2  is:

If y = –2f(– 1/3 (x + 2))^2 – 4 = -2/(9 (x + 2)^2) - 4

If x = 1 => -2/(9 (x + 2)^2) - 4 = -2/81 - 4 = -326/81

If x = 2 => -2/(9 (x + 2)^2) - 4 = -578/144

If x = 3 => -2/(9 (x + 2)^2) - 4 = -902/225