Question

unit test
unit test complete
a piecewise function f(x) is defined as shown.
$f(x) = \

$$\begin{cases} -\\frac{5}{4}x + 90, & 0 \\leq x < 40 \\\\ -\\frac{3}{8}x + 75, & 40 \\leq x \\leq 200 \\end{cases}$$

$
which table could be used to graph a piece of the function?
(then four tables with x and y values are shown, and the question is to choose the correct table.)
mark this and return
save and exit next

Explanation:

Step1: Check first piece domain

First piece: $0 \leq x < 40$, formula $\frac{-5}{4}x + 90$.

Step2: Test x=0

$y=\frac{-5}{4}(0)+90=90$ (matches first table).

Step3: Test x=16

$y=\frac{-5}{4}(16)+90=-20+90=85$ (matches first table).

Step4: Test x=40 (second piece start)

Second piece: $40 \leq x \leq 200$, formula $\frac{-3}{8}x +75$. $y=\frac{-3}{8}(40)+75=-15+75=75$ (matches first table).

Step5: Verify other tables

Second table x=40: $\frac{-3}{8}(40)+75≠40$; third table x=120: $\frac{-3}{8}(120)+75=-45+75=30$ (but x=40 y=75 is correct, but first table covers both pieces' connection); fourth table x=40: $\frac{-3}{8}(40)+75≠60$. So first table is valid.

Answer:

The first table (x: 0,16,40; y:90,85,75)