Question

Identify how the graph is transformed from that of the parent function.
y = cot(x/5)
>
DONE
y=1/4tan(x)
DONE

Answer 1

The graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation.

How to comparent a parent function with a child function

Let be $f(x) = \cot \frac{x}{5}$ the parent function and $g(x) = \frac{1}{4}\cdot \tan x$ the child function. We can obtain the child function by applying the following three steps:

1. Relationship between tangent and cotangent functions: $f'(x) = \frac{1}{f(x)} = \frac{1}{\cot \frac{x}{5} } = \tan \frac{x}{5}$
2. Dilation of the independent variable by 5: $f''(x) = f(5\cdot x) = \tan x$
3. Vertical dilation by $\frac{1}{4}$: $g(x) = \frac{1}{4}\cdot f''(x) = \frac{1}{4}\cdot \tan x$

In consequence, the graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation. $\blacksquare$

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Answer 2

Answer: first is stretched horizontally, second is compressed vertically

Step-by-step explanation: