Building Functions
How to find an explicit expression:
When given a set of numbers, such as 5, 10, 15, 20, 25... you must first look to see if there is a pattern between the numbers. In this case, there is. It is increasing at a constant rate, so we know it's linear. To write the function, we must first find the slope, using this formula:
When given a set of numbers, such as 5, 10, 15, 20, 25... you must first look to see if there is a pattern between the numbers. In this case, there is. It is increasing at a constant rate, so we know it's linear. To write the function, we must first find the slope, using this formula:
Y being the position of each number and x being the number. Now, we find the y-intercept. To do this, we plug in the slope into the equation y=mx+b, slope being m, and x being the number in the sequence we are trying to find. You can plug in any number, then solve for b, the y-intercept.
y=1/5x+b
2=1/5(10)+b
2=2+b
Subtract 2 from each side..
0=b
2=1/5(10)+b
2=2+b
Subtract 2 from each side..
0=b
Now, we put the numbers in explicit form.
tn=1/5n
How to find recursive process:
Using the same set of numbers, 5, 10, 15, 20, 25... we first need the first number, so, t1=5. Next, look at the numbers and see how to get from one to the next. In this case, we add five. The formula will look like this:
Using the same set of numbers, 5, 10, 15, 20, 25... we first need the first number, so, t1=5. Next, look at the numbers and see how to get from one to the next. In this case, we add five. The formula will look like this:
t1=5
tn=tn-1+5
tn=tn-1+5
Combining Functions:
You are given tables, all you basically do is combine functions.
You are given tables, all you basically do is combine functions.
x n(x) a(x)
1 4 5
2 8 7
3 13 11
4 15 9
1 4 5
2 8 7
3 13 11
4 15 9
Find y(x) when y(x)=n(x)+a(x)
x y(x)
1 9
2 15
3 24
4 24
1 9
2 15
3 24
4 24
Find g(x) when g(x)=n(x)-a(x)
x g(x)
1 -1
2 1
3 2
4 6
1 -1
2 1
3 2
4 6
Find h(x)when h(x)=g(x)+y(x)
x h(x)
1 8
2 16
3 26
4 30
1 8
2 16
3 26
4 30
Find t(x) when t(x)=n(x)a(x)
x g(x)
1 20
2 56
3 143
4 135
1 20
2 56
3 143
4 135
Vertical Translations:
In a vertical translation, a line is moved up or down a certain number of spaces.
In a vertical translation, a line is moved up or down a certain number of spaces.