CHAPTER 12. HYPERBOLIC FUNCTIONS ANDGRAPHS 12.2
For example, sketch thegraph of g(x) =x+1^2 + 2. Mark the intercepts and asymptotes.
We have determined the domain to be{x : x∈R, x�=− 1 } and the range to be{g(x) : g(x)∈
(−∞;2)∪ (2;∞)}. Therefore the asymptotes are at x =− 1 and y = 2. The y-intercept = 4 and the
x-intercept =− 2.
1
2
3
4
5
6
− 1
− 2
− 3
4 3 − 2 − − 1 − 1 2 3 4
Figure 12.2: Graph of g(x) =x^2 +1+ 2.Exercise 12 - 4
- Draw the graph of y =^1 x+ 2. Indicate the horizontalasymptote.
- Given: h(x) =x+4^1 − 2. Sketch the graph of h showing clearly the asymptotes and ALL intercepts
with the axes. - Draw the graph of y =^1 xand y =−x^8 +1+ 3 on the same system of axes.
- Draw the graph of y =x−^52 , 5 + 2. Explain your method.
- Draw the graph of the function defined by y =x−^88 + 4. Indicate the asymptotes and intercepts
with the axes.