Which of the following are the domain and range that represent the inverse of the function f(x), given the mapping diagram of f(x) below

The domain of the original function is:
 Domain: {1,2,3,4}
 The range of the original function is:
 Range: {2,4,6,8}

 The inverse of the function f (x) is that function that fulfills:
 1) The domain of f(x)^-1 is the range of the function f (x)
 2) The range of f(x)^-1 is the domain of the function f (x)

 We have then that the domain of the inverse function is:
 Domain: {2,4,6,8}
 The range of the inverse function is:
 Range: {1,2,3,4}

 
 Option 1

Answer: choice c and choice d

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

The first digit is in the middle school 100s place