Question

if the cosine function is stretched by a factor of 10, what will the resulting function f(x) be? (1 point)
○ f(x) = cos(\frac{x}{20})
○ f(x) = cos(10x)
○ f(x) = cos(20x)
○ f(x) = cos(\frac{x}{10})

Explanation:

Step1: Recall the horizontal stretch rule

For a function \(y = f(x)\), a horizontal stretch by a factor \(a\) gives \(y = f(\frac{x}{a})\).

Step2: Apply the rule to the cosine function

The original function is \(y=\cos(x)\). Stretching it by a factor of \(10\) (i.e., \(a = 10\)), we substitute \(x\) with \(\frac{x}{10}\) in the cosine function. So the new function is \(f(x)=\cos(\frac{x}{10})\).

Answer:

\(f(x)=\cos(\frac{x}{10})\) (the fourth option)