How many of the relations are functions? I’m mainly debating if the first and fourth graphs are functions or not...

A relation f(x) is a function only when there is not two different values in the range that are related to the same value in the domain.

This means that does not exist y1 and y2 such:

f(x1) = y1

f(x1) = y2

if this happens, f is not a function.

Upper graphs, from left to right.

the first graph is a constant line, this is a function f(x) = c.

The second graph is not a function.

The third graph is not a function

the fourth graph is a function

the fourth graph is a function

the fifth graph is not a function.

From the lower ones:

The set of data can be a function

y = 2x^2 - 3 is a function.

The diagram with two circles is not a function (there are more than one output for some imputs)

The last table is a function

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt