Given the function $f(x) = x^2$, if its graph is transformed by a vertical stretch by a factor of $2$, a reflection across the y-axis, and a horizontal shift left by $3$ units, what is the resulting equation?
Question 2
If the graph of $y = f(x)$ is transformed to $y = -3f(2x - 4) + 1$, what is the correct sequence of transformations, considering the order of operations?
Question 3
Given the function $f(x) = e^x$, what is the equation of the function after a vertical compression by a factor of $1/2$, a reflection across the y-axis, and a horizontal shift right by $4$ units?
Question 4
The graph of $y = \sqrt{x}$ is transformed by a horizontal stretch by a factor of $3$, a reflection across the x-axis, and a vertical shift down by $2$ units. What is the resulting equation?
Question 5
If the function $f(x) = \sin(x)$ is transformed to $g(x) = -\sin(2x + \pi) + 3$, what are the transformations applied to $f(x)$?
