Question

the graph of $y = |x|$ is scaled vertically by a factor of $\frac{1}{3}$. what is the equation of the new graph? choose 1 answer: a $y = |x| - 3$ b $y = -3|x|$ c $y = \frac{1}{3}|x|$ d $y = |x| - \frac{1}{3}$

Explanation:

Step1: Recall vertical scaling rule

For a function \( y = f(x) \), a vertical scaling by a factor of \( k \) gives \( y = kf(x) \). Here, \( f(x)=\vert x\vert \) and \( k = \frac{1}{3} \).

Step2: Apply the scaling rule

Substitute \( f(x)=\vert x\vert \) and \( k=\frac{1}{3} \) into \( y = kf(x) \), we get \( y=\frac{1}{3}\vert x\vert \).

Answer:

C. \( y = \frac{1}{3}\vert x\vert \)