Relations & Functions
Graphical Transformations
Grade 12
Question:
<p><strong>Ex. 11</strong> The graph of \(f(x)\) is given. Which of the following represents the graph of \(-f(x) + 2\)?</p>
<p>(a) Graph showing reflection over x-axis and vertical shift up by 2</p>
<p>(b) Graph showing horizontal shift and reflection</p>
<p>(c) Graph showing reflection over y-axis</p>
<p>(d) Graph showing horizontal and vertical shifts</p>
Step-by-Step Solution
Key Concept: Transformation -f(x) reflects the graph across the x-axis, and adding 2 shifts it vertically upward by 2 units.
<p><strong>Solution:</strong> To obtain the graph of $-f(x) + 2$ from $f(x)$:</p><p><strong>Step 1:</strong> Apply $-f(x)$: Reflect the graph of $f(x)$ about the x-axis.</p><p><strong>Step 2:</strong> Apply the transformation $-f(x) + 2$: Shift the reflected graph vertically upward by 2 units.</p><p>The resulting graph shows a reflection of $f(x)$ across the x-axis followed by a vertical translation of 2 units upward.</p>
Correct Answer: a