Question

question 8 (multiple choice worth 1 points)
(translating quadratic functions mc)

if \\(h(x) = g(x) - 16\\), how does the graph of \\(h(x)\\) compare to the graph of \\(g(x)\\)?

• the function \\(g(x)\\) is translated 16 units upward to form \\(h(x)\\).
• the function \\(g(x)\\) is translated 16 units downward to form \\(h(x)\\).
• the function \\(g(x)\\) is translated 16 units to the right to form \\(h(x)\\).
• the function \\(g(x)\\) is translated 16 units to the left to form \\(h(x)\\).

Explanation:

Analyze the transformation rule

Using the Function Transformations knowledge point

$$ h(x) = g(x) - 16 $$

Determine the direction of translation

Using the Function Transformations knowledge point

$$ \text{Subtracting } 16 \text{ from } g(x) \text{ shifts the graph vertically downward by } 16 \text{ units.} $$

Answer:

• The function g(x) is translated 16 units upward to form h(x).
• The function g(x) is translated 16 units downward to form h(x). (Correct answer)
• The function g(x) is translated 16 units to the right to form h(x).
• The function g(x) is translated 16 units to the left to form h(x).