What do graphs of functions have in common?
1 answer:
You might be interested in
Math is about number sense and matching patterns. You get number sense by playing with numbers: counting, arranging. Most people do not find it difficult to match patterns, as our brains are wired to see them--sometimes even when they aren't there.
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C
Answer:
The y-intercept of the function is: b=10
Step-by-step explanation:
Given the table
x y
1 8
2 6
3 4
4 2
Taking any two points to find the slope
- (1, 8)
- (2, 6)
The slope between (1, 8) and (2, 6) is:
We know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept.
Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).
8 = -2(1) + b
8 = -2 + b
b = 8+2
b = 10
Thus, the y-intercept of the function is: b=10