Question

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

Answer 1

The last table with x and y values:

x y

40 60

160 15

200 0

is the correct table

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:
`40\leq x\leq 200` ) :
`f(x)=-(3)/(8) x+75`,

which therefore gives :
`f(40)=-(3)/(8) (40)+75= -15+75=60`

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:
`40\leq x\leq 200`

`f(160)=-(3)/(8) (160)+75= -60+75=15`

so, this pair is also correct.

Now the last check (for x = 200):

`f(200)=-(3)/(8) (200)+75= -75+75=0`

which also checks with the values in the given table.