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For each function, state whether it is linear, quadratic, or exponential.




Function 1
Function 2
Function 3



x

y

x

y

x

y


3
35
1
9
2
-8


4
25
2
7
3
-16


5
18
3
9
4
-24


6
14

bar(4)
15

bar(5)



7
13

sqrt5
25

bar(6)
-40


Linear
Linear
Linear


Quadratic
Quadratic
Quadratic


Exponential
Exponential
Exponential


None of the above
None of the above
None of the above

For each function, state whether it is linear, quadratic, or exponential.\newline\newlineFunction 11\newlineFunction 22\newlineFunction 33\newline\newlinexx\newlineyy\newlinexx\newlineyy\newlinexx\newlineyy\newline\newline33\newline3535\newline11\newline99\newlineyy00\newlineyy11\newline\newlineyy22\newlineyy33\newlineyy00\newlineyy55\newline33\newlineyy77\newline\newlineyy88\newlineyy99\newline33\newline99\newlineyy22\newlinexx33\newline\newlinexx44\newlinexx55\newline\bar{44}\(\newline\)\(x\)\(6\)\(\newline\)\bar{\(5\)}\newline\newlineyy55\newlinexx88\newlinexx99\newlineyy33\newline\bar{66}$\(\newline\)\(y\)\(1\)\(\newline\)\(\newline\)Linear\(\newline\)Linear\(\newline\)Linear\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Exponential\(\newline\)Exponential\(\newline\)Exponential\(\newline\)None of the above\(\newline\)None of the above\(\newline\)None of the above

Full solution

Q. For each function, state whether it is linear, quadratic, or exponential.\newline\newlineFunction 11\newlineFunction 22\newlineFunction 33\newline\newlinexx\newlineyy\newlinexx\newlineyy\newlinexx\newlineyy\newline\newline33\newline3535\newline11\newline99\newlineyy00\newlineyy11\newline\newlineyy22\newlineyy33\newlineyy00\newlineyy55\newline33\newlineyy77\newline\newlineyy88\newlineyy99\newline33\newline99\newlineyy22\newlinexx33\newline\newlinexx44\newlinexx55\newline\bar{44}\(\newline\)\(x\)\(6\)\(\newline\)\bar{\(5\)}\newline\newlineyy55\newlinexx88\newlinexx99\newlineyy33\newline\bar{66}$\(\newline\)\(y\)\(1\)\(\newline\)\(\newline\)Linear\(\newline\)Linear\(\newline\)Linear\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Exponential\(\newline\)Exponential\(\newline\)Exponential\(\newline\)None of the above\(\newline\)None of the above\(\newline\)None of the above
  1. Analyze Function 11: Analyze Function 11 by checking the differences in y-values as xx increases by 11. Calculate the differences: 3525=1035-25=10, 2518=725-18=7, 1814=418-14=4, 1413=114-13=1.
  2. Identify Quadratic Pattern: Notice the differences between consecutive yy-values are decreasing, suggesting a non-linear pattern. Check second differences: 710=37-10=-3, 47=34-7=-3, 14=31-4=-3.
  3. Analyze Function 22: Since the second differences are constant, Function 11 is quadratic.
  4. No Consistent Pattern: Analyze Function 22 by checking the yy-values directly given the xx-values. Notice yy-values: 99, 77, 99, 1515, 2525.
  5. Analyze Function 33: Observe that yy-values do not follow a consistent pattern of change, either linear or quadratic. Check for exponential pattern by ratios: 79\frac{7}{9}, 97\frac{9}{7}.
  6. Identify Pattern: Ratios are not consistent, indicating Function 22 is neither linear, quadratic, nor exponential.
  7. Identify Pattern: Ratios are not consistent, indicating Function 22 is neither linear, quadratic, nor exponential. Analyze Function 33 by checking the yy-values. Notice yy-values: 8-8, 16-16, 24-24, 40-40.
  8. Identify Pattern: Ratios are not consistent, indicating Function 22 is neither linear, quadratic, nor exponential. Analyze Function 33 by checking the yy-values. Notice yy-values: 8-8, 16-16, 24-24, 40-40. Calculate the differences: 16(8)=8-16 - (-8) = -8, 24(16)=8-24 - (-16) = -8, 40(24)=16-40 - (-24) = -16.

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