right and 1 unit down.\nquestion 13 (1 point)\nlisten\nwhich equation represents the graph of ( y = f(x) )…

right and 1 unit down.\nquestion 13 (1 point)\nlisten\nwhich equation represents the graph of ( y = f(x) ) after it is translated 4 units to the right and then compressed horizontally by a factor of ( \frac{1}{2} )?\n( \bigcirc ) a) ( y = fleft(\frac{x - 4}{2}\right) )\n( \bigcirc ) b) ( y = fleft(\frac{x}{2}-4\right) )\n( \bigcirc ) c) ( y = f(2x - 4) )\n( \bigcirc ) d) ( y = f(2x - 8) )

right and 1 unit down.\nquestion 13 (1 point)\nlisten\nwhich equation represents the graph of ( y = f(x) ) after it is translated 4 units to the right and then compressed horizontally by a factor of ( \frac{1}{2} )?\n( \bigcirc ) a) ( y = fleft(\frac{x - 4}{2}\right) )\n( \bigcirc ) b) ( y = fleft(\frac{x}{2}-4\right) )\n( \bigcirc ) c) ( y = f(2x - 4) )\n( \bigcirc ) d) ( y = f(2x - 8) )

Answer

Explanation:

Step1: Horizontal translation

For a function (y = f(x)), translating (a) units to the right gives (y=f(x - a)). Here (a = 4), so the function becomes (y=f(x - 4)).

Step2: Horizontal compression

For a function (y = f(x)), a horizontal compression by a factor of (k) ((k>1)) is given by replacing (x) with (kx). Here (k = 2) (since compression by a factor of (\frac{1}{2}) means (x\to2x)). Substitute (x) in (y = f(x - 4)) with (2x). We get (y=f(2x-4)).

Answer:

C. (y = f(2x - 4))