Question

which of the following accurately describes a transformation to the parent function that results in $h(x) = -8.2cos x$? (1 point)
the graph of the parent function is horizontally translated down 8.2 units.
the maximum of the parent function was changed from 1 to -8.2.
the graph of the parent function is vertically compressed by 8.2.
the graph of the parent function is vertically stretched by 8.2.
check answer remaining attempts : 3

Explanation:

For a function \(y = A\cos(x)\), the amplitude is \(|A|\). When \(|A|> 1\), the graph of \(y=\cos(x)\) (parent function) is vertically stretched by a factor of \(|A|\). Here \(A=-8.2\), and \(|A| = 8.2>1\).

Horizontal translation down \(k\) units would be of the form \(y=\cos(x)-k\), which is not the case here.

The maximum of \(y = \cos(x)\) is \(1\), for \(y=-8.2\cos(x)\), the maximum is \(8.2\) (since \(\cos(x)\) ranges from \(- 1\) to \(1\), \(-8.2\cos(x)\) ranges from \(-8.2\) to \(8.2\)).

Vertical compression occurs when \(0<|A|<1\).

Answer:

The graph of the parent function is vertically stretched by 8.2.