Determine the type of function each table represents. Write “linear”, “exponential”, or “neither”. Two-way table with x-values 0, 1, 2, 3, 4 and y-values 0, 1, 4, 9, 16
[ Select ]

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 1/3, 1, 3, 9, 27
[ Select ]

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 5, 5/2, 5/4, 5/8, 5/16
[ Select ]

Two-way table with x-values 0, 1, 2, 3, 4 and y-values 4.5, 4, 3.5, 3, 2.5
[ Select ]

1) Neither

2) Exponential

3) Exponential

4) Linear

Step-by-step explanation:

1) x-values       y-values

0                          0

1                           1

2                          4

3                           9

4                          16

Therefore, we have, the relationship of the function given as_f(x) = x² Which is neither a linear function nor an exponential function

2) x-values       y-values

0                          1/3

1                           1

2                          3

3                           9

4                          27

The relationship between 'x', and 'y' is given as follows;

f(x) = 3⁽ˣ⁻¹⁾

Therefore, the relationship between 'x', and 'y', is an exponential relationship, and the function is an exponential function

3) x-values       y-values

0                           5

1                           5/2

2                          5/4

3                           5/8

4                          5/16

The relationship between 'x', and 'y' is given as follows;

f(x) = 5×(1/2)ˣ

Therefore, the relationship between 'x', and 'y', is an exponential relationship, and the function is an exponential function

4) x-values       y-values

0                           4.5

1                           4

2                          3.5

3                           3

4                          2.5

The given data for the y-values has a constant first common difference of 4 - 4.5 = -0.5, therefore, the relationship between the 'x', and 'y' values is a linear relationship.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

b.

step-by-step explanation:

i just know