Question

the graph of $y = |x|$ is scaled vertically by a factor of 6. what is the equation of the new graph? choose 1 answer: a $y = |x - 6|$ b $y = 6|x|$ c $y = \frac{1}{6}|x|$ d $y = \left|x - \frac{1}{6}\
ight|$

Explanation:

Step1: Recall vertical scaling rule

For a function \( y = f(x) \), vertical scaling by a factor \( k \) gives \( y = k \cdot f(x) \).
Here, \( f(x)=|x| \) and \( k = 6 \).

Step2: Apply the scaling

Substitute \( f(x)=|x| \) and \( k = 6 \) into \( y = k \cdot f(x) \), we get \( y = 6|x| \).

Answer:

B. \( y = 6|x| \)