Question

the graph of $y = |x|$ is shifted down by 6 units and to the left by 9 units.
what is the equation of the new graph?
choose 1 answer:
a $y = |x + 9| + 6$
b $y = |x + 9| - 6$
c $y = |x - 9| + 6$
d $y = |x - 9| - 6$

Explanation:

Step1: Recall transformation rules

For a function \( y = f(x) \), shifting left by \( h \) units (where \( h>0 \)) gives \( y = f(x + h) \), and shifting down by \( k \) units (where \( k>0 \)) gives \( y = f(x)-k \).

Step2: Apply horizontal shift

The original function is \( y = |x| \). Shifting left by 9 units, we replace \( x \) with \( x + 9 \), so the function becomes \( y = |x + 9| \).

Step3: Apply vertical shift

Now, shifting down by 6 units, we subtract 6 from the function. So the new function is \( y = |x + 9|-6 \).

Answer:

B. \( y = |x + 9| - 6 \)