A piece wide function f(x) is defined as shown f(x) = { -5/4x + 90, 0 < x < 40 { -3/8x + 75, 40 < x < 200 which table could be used to graph a piece of the function? HELP

The last table with x and y values:

x       y

40    60

160   15

200   0

is the correct table

Step-by-step explanation:

Notice that the x-value 40 appears in all four tables, so let's use it according to the piece-wise function definition to decide which table can be the true one.

Notice that from the function's description, when x = 40 the function that should be used is (its domain includes 40 according to: ) : ,

which therefore gives :

therefore, we know that the only table that shows a y-value of 60 associated with x=40 is the last table. We should check that the other two pairs are also correct before deciding for it:

Is f(160) = 15 , and is f(200) = 0 according to the function's definition?

Let;s calculate f(160) (for which we need to use again the second function given which is valid for x values such that:

so, this pair is also correct.

Now the last check (for x = 200):

which also checks with the values in the given table.

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