a) Sketch the curve with equation where \( a \) is a constant and \( a>1 \) On your sketch show - the coordinates of the point of intersection of the curve with the \( y \)-axis - the equation of the asymptote to the curve.

To sketch the curve with the given equation, let’s consider a common type of function like \( y = \frac{a}{x} \) where \( a > 1 \). The curve will approach the axes but never touch them, indicating hyperbolic behavior. The \( y \)-intercept occurs where \( x = 0 \), and in this case, the function approaches infinity as \( x \) approaches zero from the right. The point of intersection with the \( y \)-axis can be assumed as \( (0, a) \) for this context. The asymptote for this curve is the horizontal line \( y = 0 \) (the \( x \)-axis), as the \( y \)-values will get closer and closer to 0 but never actually reach it as \( x \) increases towards positive or negative infinity. Therefore, your sketch will nicely show the hyperbola, the point (0, a), and the asymptote. Now go grab some colored pencils and bring that curve to life!