Question

How do you describe the sequence of transformations of `y = -2tan(x+(pi/4))`?

Answer 1

Shift the graph of tangent `pi/4` to the left, stretch the graph vertically by a factor of 2, reflect the resulting graph over the `x`-axis.

Explanation:

For the horizontal shift I always take whatever is in the parentheses find what makes it 0: `x+pi/4=0\rightarrowx=-pi/4`, so we need to shift `pi/4` to the left.

The absolute value of the coefficient of the function is a vertical stretch, in this case by a factor of 2. The negative sign reflects over the `x`-axis.