Question

value: 1

which of the following statements is true for the function \\(y = 20\sqrt{x}\\)?

a. the graph is vertically stretched.
b. the graph is vertically compressed.
c. the graph is horizontally stretched.
d. the graph is horizontally compressed.

Explanation:

Identify the parent function and transformation

The parent function is \(f(x) = \sqrt{x}\). The given function is \(y = 20\sqrt{x}\), which is in the form \(y = a \cdot f(x)\) where \(a = 20\).

Analyze the transformation factor

Since \(a = 20\) and \(|a| > 1\), multiplying the function by a factor of 20 results in a vertical stretch.

Answer:

• a. The graph is vertically stretched. (Correct answer)
• b. The graph is vertically compressed.
• c. The graph is horizontally stretched.
• d. The graph is horizontally compressed.