Given the function defined by f(x)=6/x-3 2.1 Write down the equations of the asymptotes of f. 2.2 Determine the x intercept of f. 2.3 Sketch the graph of f. Show clearly the intercepts with the axis and the asymptote. 2.4 Write down the equation of the line of symmetry with negative gradient.

The function \( f(x) = \frac{6}{x} - 3 \) has a vertical asymptote at \( x = 0 \) (where the denominator is zero) and a horizontal asymptote at \( y = -3 \) (as \( x \) approaches \( \pm \infty \)). These two asymptotes indicate that the function does not cross these lines, providing boundaries for the graph. To find the \( x \)-intercept, we set \( f(x) = 0 \): \( \frac{6}{x} - 3 = 0 \). Solving this yields \( \frac{6}{x} = 3 \) or \( x = 2 \). Therefore, the \( x \) intercept is \( (2, 0) \). The function can be sketched by plotting the asymptotes and the intercept, demonstrating its behavior in the quadrants around the asymptotes. The line of symmetry for this function, given its nature, would not typically accommodate a line of symmetry since it's a hyperbolic function; however, we can note the general trend that functions of this type do not reflect symmetrically across a line but can possess other symmetries.