Given the function: \( h(x)=-\frac{2}{x-2}+2 \). \( 5.1 \quad \) Write down the equations of the asymptotes of \( h \). 5.2 Draw the graph of \( h \). Clearly show all asymptotes and intercepts with the axes. 5.3 Determine the equation of the axis of symmetry of \( h \) with \( m<0 \).

To find the equations of the asymptotes of \( h(x) = -\frac{2}{x-2} + 2 \): 1. **Vertical Asymptote**: This occurs where the denominator is zero, leading to infinite values. Here, \( x - 2 = 0 \) gives us the vertical asymptote at \( x = 2 \). 2. **Horizontal Asymptote**: As \( x \) approaches infinity, the term \( -\frac{2}{x-2} \) trends toward \( 0 \). Thus, \( h(x) \) approaches \( 2 \), giving us the horizontal asymptote at \( y = 2 \). Now for a visual representation: Plotting the function, you will see that the graph approaches \( y = 2 \) as \( x \) goes to negative or positive infinity, and it shoots up or down when nearing \( x = 2 \) (the vertical asymptote). The intercepts are found by setting \( h(x) = 0 \) and finding \( x \)-intercepts and setting \( x = 0 \) for \( y \)-intercepts. The axis of symmetry for rational functions generally involves determining where the function flips, which can be tricky. However, since \( m < 0 \) usually implies a reflection along the vertical axis. Here, \( x = 2 \) acts like an axis of symmetry, but remember to check that it implies your function matches this reflective property through substitution or analysis of its behavior relative to the defined line.