photo.jpg

# Curve Sketching A curve gives a geometrical interpretation of a function. It gives a picture of the function, based on its properties. The frequent use made in this chapter of curve sketching shows the importance of this in mathematics. To successfully trace or sketch a curve, we need the knowl...

# Curve Sketching A curve gives a geometrical interpretation of a function. It gives a picture of the function, based on its properties. The frequent use made in this chapter of curve sketching shows the importance of this in mathematics. To successfully trace or sketch a curve, we need the knowledge of the following: - The intercepts - The asymptotes - Variation table - Excluded regions - Symmetry - Range of values - Turning points or stationary points ### Intercepts There are 2 intercepts, x and y intercept. At y-intercept, x = 0 and at x-intercept, y = 6. ### Asymptotes There are 3 types of asymptotes: vertical, horizontal, and oblique, or, slant or inclined asymptotes. **Note:** Asymptotes are lines that your curve approaches, but never touches. In other words, an asymptote is a line that becomes a tangent to a curve as x or y → ∞. ### Conditions for the existence of an asymptote Most rational functions have a vertical asymptote. For a function for $f(x) = \frac{g(x)}{h(x)}$, when the equation h(x) = 0 has real solutions, then the function has a vertical asymptote, and vice versa. If the equation h(x) = 0 does not have real solutions, then h(x) does not have a vertical asymptote.