The equation of the transformed function is y = 5cos(x/4 + 60) - 3
The equation of the graph is given as:
y = cos(x)
The rule of downward shift is:
(x, y) ⇒ (x, y - h)
So, the function when shifted downwards by 3 units is
y = cos(x) - 3
The rule of horizontal shrink is:
(x, y) ⇒ (x/k, y)
So, the function when shrink horizontally by a fourth unit is:
y = cos(x/4) - 3
The rule of left shift is:
(x, y) ⇒ (x +h, y)
So, the function when shifted left by 60 units is
y = cos(x/4 + 60) - 3
The amplitude is given as:
A= 5
So, we have:
y = 5cos(x/4 + 60) - 3
Hence, the equation of the transformed function is y = 5cos(x/4 + 60) - 3
Read more about function transformation at:
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