Question

the graph of $y = |x|$ is scaled vertically by a factor of $\frac{7}{2}$. what is the equation of the new graph? choose 1 answer: a $y = -\frac{2}{7}|x|$ b $y = -\frac{7}{2}|x|$ c $y = \frac{2}{7}|x|$ d $y = \frac{7}{2}|x|$

Explanation:

Step1: Recall vertical scaling rule

For a function \( y = f(x) \), vertical scaling by a factor \( k \) gives \( y = kf(x) \). Here, \( f(x)=|x| \) and \( k = \frac{7}{2} \), and there's no reflection (since the factor is positive, no negative sign).

Step2: Apply the rule

Substitute \( f(x)=|x| \) and \( k = \frac{7}{2} \) into \( y = kf(x) \), we get \( y=\frac{7}{2}|x| \).

Answer:

D. \( y = \frac{7}{2}|x| \)