LESSON
Advanced Algebra 2 Practice A 6.7
Modeling Real-World Data
Determine which parent function would best model the given data set. Choose among linear, quadratic, exponential, and square root.
1. a. Look at the table at right. Are the
data for one variable evenly spaced?
b. Look at the data for the other variable.
Which differences, if any, are constant?
c. Which parent function best models the data?
2. 3. 4.
Write a function that models the given data.
5. Use a graphing calculator to make a
scatter plot. Then use the regression
feature to find the function that best
represents the data.
Solve.
6. The table shows the number of sport utility vehicles sold in the United States
from 1997 to 2003. Write a function that models the data.
|Years after 1996 |1 |2 |3 |4 |5 |6 |7 |
|SUVs (millions) |2.3 |2.8 |3.1 |3.2 |3.8 |4.0 |4.3 |
6. y ’ 2x + 1
x ’ 2y + 1
x − 1 ’ 2y
[pic]
domain: all real numbers; range: all real numbers
Challenge
1. Linear functions with a nonzero slope are always one-to-one.
2. Linear functions with a nonzero slope are always one-to-one.
3. Not one-to-one; fails the horizontal line test; also try [pic] and [pic] for a and b.
4. One-to-one
5. Fails horizontal line test, not one-to-one
6. Not one-to-one, f(−2) ’ f(0)
7. Not one-to-one; f(0) ’ f(1) ’ 0
8. One-to-one
9. Not one-to-one since (3, 5) is not equal to (4, 5) but max(3, 5) ’ 5 ’ max(4, 5)
Problem Solving
1. a. L(h) ’ 2.5( h; [pic]
b. h(L) gives the height of a can for a given lateral surface area.
c. 4.5 in.
2. C 3. F
4. B 5. J
Reading Strategies
1. The inverse is not a function. The graph of f is a horizontal line. So the horizontal line y ’ 3 intersects the graph of f at infinitely many points.
2. If the slope is not 0, then the graph is a straight line inclined at an angle. All horizontal lines will intersect the graph at only one point, so these graphs will all have inverse relations that are functions.
3. a. The line y ’ 4 will intersect the function at least at two points.
b. No; the function fails the horizontal-line test.
4. The vertical-line test should be used to test whether the graph represents a function.
Modeling Real-World Data
PRACTICE A
1. a. Yes, the y-values
b. Second differences
c. Square root function
2. Quadratic 3. Linear
4. Exponential 5. f(x) ’ −0.5x2 + 10
6. f(x) ’ 0.33x + 2.06
Practice B
1. Exponential 2. Linear
3. Quadratic 4. Square root
5. f(x) ’ 2x2 − 9 6. f(x) ’ −0.4x + 6
7. f(x) ’ 2.18(1.577)x 8. f(x) ’ 0.816[pic]
9. f(x) ’ 0.44x2 + 0.2x + 0.36
10. f(x) ’ 1.318x0.378
11. a. f(x) ’ 657.3(1.02)x
b. 1634 people
Practice C
1. Quadratic 2. Exponential
3. f(x) ’ 4(0.5)x 4. f(x) ’ −0.8x + 2.3
5. f(x) ’ 2.045x0.336 6. f(x) ’ 0.88x0.597
7. f(x) ’ 940(0.15)x
8. f(x) ’ −x2 + 0.35x + 0.8
9. a. f(x) ’ 2.15(1.1)x
b. 720 billion shares
c. 1966
Reteach
1. Linear model
2. Square root model 3. Yes
-----------------------
|x |y |
|5 |1 |
|8 |2 |
|13 |3 |
|20 |4 |
|29 |5 |
|40 |6 |
|x |y |
|1 |−2 |
|2 |4 |
|3 |−8 |
|4 |16 |
|5 |−32 |
|6 |64 |
|x |y |
|8 |−26 |
|16 |−2 |
|24 |22 |
|32 |46 |
|40 |70 |
|x |y |
|2 |84 |
|4 |72 |
|6 |52 |
|8 |24 |
|10 |−12 |
|12 |−56 |
|x |−2 |0 |2 |4 |6 |
|y |8 |10 |8 |2 |−8 |
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