Functions
Graph Transformation
MMTS_Full_Test_15
Grade 12
Question:
Graph of $y=f(x)$ is given with $f(0)=3$, minimum at $x=1$, zero at $x=-1$ and $x=3$. Then graph of $y=\dfrac{-1}{|f(x)|}$ is best represented by:
Option 1
Option 2
Option 3
Option 4
Step-by-Step Solution
Key Concept: $\frac{-1}{|f|}$: negative, zeros of $f$ become vertical asymptotes, max of $|f|$ becomes least negative value
$-1/|f(x)|$ is always $\le 0$; asymptotes at $x=-1$ and $x=3$; passes through $(0,-1/3)$. This matches option 3.
Correct Answer: 3