06Hfurthergraphs

toc = Further Graphs =

We studied graphing the sum, difference and product of two functions in Chapter 2. (see here) These processes can also be applied to trigonometric graphs.

Recall that a combined graph is only defined when both of its component graphs are defined. Hence: math domain(f \pm g) = domain(f) \cap domain(g) math

** Example 1 **
Sketch 2sin(x) + cos(2x) by addition of ordinates in the domain x Î [0, 2 p ]

{Sketch **y1 = 2sin(x)** and **y2 = cos(2x)** then add key points. Final graph is in red}



Addition of ordinates gives us some of the key points. We would have to use algebra or technology to find the rest (x-intercepts and maximum stationary points).

Absolute Value Graphs
We introduced graphs involving the absolute value function in Chapter 2 (see here).

Recall that to draw y = |f(x)|, first draw y = f(x) then reflect anything below the x-axis up above the x-axis.

** Example 2 **
Sketch y = |2sin(x) + 1| for x Î [0, 4 p ]



x-intercepts (and cusp points) at: math \dfrac{7\pi}{6},\;\dfrac{11\pi}{6},\;\dfrac{19\pi}{6},\;\dfrac{23\pi}{6} math

Maximum stationary points at: math \left(\dfrac{\pi}{2},\;3\right),\;\left(\dfrac{3\pi}{2},\;1\right),\;\left( \dfrac{5\pi}{2},\;3\right),\;\left(\dfrac{7\pi}{2},\;1\right) math Go to top of page flat .