Question

right and 1 unit down.
question 13 (1 point)
listen
which 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} )?
( \bigcirc ) a) ( y = fleft(\frac{x - 4}{2}
ight) )
( \bigcirc ) b) ( y = fleft(\frac{x}{2}-4
ight) )
( \bigcirc ) c) ( y = f(2x - 4) )
( \bigcirc ) d) ( y = f(2x - 8) )

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