Answer:
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: [tex]40\leq x\leq 200[/tex] ) : [tex]f(x)=-\frac{3}{8} x+75[/tex],
which therefore gives : [tex]f(40)=-\frac{3}{8} (40)+75= -15+75=60[/tex]
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: [tex]40\leq x\leq 200[/tex]
[tex]f(160)=-\frac{3}{8} (160)+75= -60+75=15[/tex]
so, this pair is also correct.
Now the last check (for x = 200):
[tex]f(200)=-\frac{3}{8} (200)+75= -75+75=0[/tex]
which also checks with the values in the given table.
