Question

A piecewise function f(x) is defined as shown. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayout Which table could be used to graph a piece of the function? A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75. A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0. A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0. A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Answer 1

Answer:

(D)The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Step-by-step explanation:

The piece-wise function, f(x) is defined as follows:

$f(x)=\left\{\begin{array}{ccc}-\frac{5}{4}x+90 &0\leq x$

$f(0)=-\frac{5}{4}*0+90=90\\\\f(16)=-\frac{5}{4}*16+90=70\\\\f(40)=-\frac{3}{8}*40+75=60\\\\f(120)=-\frac{3}{8}*120+75=30\\\\f(160)=-\frac{3}{8}*160+75=15\\\\f(200)=-\frac{3}{8}*200+75=0$

Therefore, the table which could represent the function is that which satisfies the points above.

In option D

$\left|\begin{array}{c|c}x&f(x)\\--&--\\40&60\\160&15\\200&0\end{array}\right|$

The correct option is D