(a) \( f(x)=\frac{1}{x} \), reflect in the \( x \) axis, shift up by 3

When you reflect the function \( f(x) = \frac{1}{x} \) in the \( x \)-axis, you get \( f(x) = -\frac{1}{x} \). This transformation flips the graph upside down, turning positive values negative and vice versa. Next, when you shift this reflected function up by 3 units, you add 3 to the entire function, resulting in \( g(x) = -\frac{1}{x} + 3 \). This moves all the points of the graph up, creating a new function that maintains the shape of the original while adjusting its position on the Cartesian plane!