Building Functions
Sequence
{2,8,14,20,26,32,38}
{2,8,14,20,26,32,38}
Recursive Formula
tn= tn-1+6 |
Explicit Formula
tn=2=+6(n-1) |
I found this by knowing that the rate of change is 6 and the first term is 2.
Combining Functions
f(x)= 10x+3
|
g(x)= 3x-8
|
f(x) + g(x)
The equation first begins with adding the two functions together, obviously. You will end up with "10x+3+3x-8" as the non simplified version of the combined function. You then simplify it to "13x-5" and that's your new combined function!
f(x) - g(x)
This system of combining functions is actually very similar to the last. You first start out with "10x+3-3x-8". See how this is near the exact some function as the last exept for one minus sign instead of plus. You then simplify this and get "7x-5x". Once again, we have a combined function.
f(x) * g(x)
This is slightly different from the last two. The beginning equation would be "(10x+3)(3x-8)". Already there is some major difference as the two functions are more distinct in this equation. After multiplied, this equation becomes "30x-24" which is much different from the other equations.
f(g(x))
Now, this is completely different as you insert one entire function into another. This scenario comes out to "10(3x-8)+3". This then becomes "30x-80+3" and in turn "30x-73" as a final result.
Translations
A vertical translation is when the graph of a function is moved up or down along the y-axis. A horizontal translation is when the graph is moved to the left or right along the x-axis.