What transformations change the graph of f(x) = −x to the graph of g(x) = −0.1(x − 6)? A. vertical compression by a factor of 0.1 and a horizontal translation 6 units right
B. vertical compression by a factor of −6 and a horizontal translation −0.1 units right
C. vertical stretch by a factor of 10 and a horizontal translation 6 units left
D. horizontal compression by a factor of 0.1 and a vertical translation 6 units right

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  A. vertical compression by a factor of 0.1 and a horizontal translation 6 units right

Step-by-step explanation:

The relation between g(x) and f(x) is ...

  g(x) = 0.1·f(x -6)

The factor of 0.1 compresses the graph vertically to 1/10 of its previous height. The addition of -6 moves the graph horizontally by 6 units to the right.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !

step-by-step explanation: