Chapter 4.3, Problem 3STP

For Exercises $1-5,$ choose the correct letter.

Which rule could represent the function shown by the table at the right?

A. $y=-x^3$

B. $y=x^2+1$

c. $y=-x^2+1$

D. $y=-x-1$

To determine

Which rule among the functions $A.y=-x^3,B.y=x^2+1,C.y=-x^2+1,D.y=-x-1$ could represent the table shown as below.

x	-2	-1	0	1	2
y	-3	0	1	0	-3

Answer to Problem 3STP

The function $\left(y=-x^2+1\right)$ satisfies the given table, so option (C) is correct.

Explanation of Solution

Given information: The table for the functions $A.y=-x^3,B.y=x^2+1,C.y=-x^2+1,D.y=-x-1$ is shown as,

x	-2	-1	0	1	2
y	-3	0	1	0	-3

Calculation: From the given table satisfy the values of $\left(x\right)\text{and }\left(y\right)$ for the given functions.

  $\begin{array}{c}A.y=-x^3\\ \left(-3\right)=-{\left(-2\right)}^3\mathrm{....}\left(\text{For }x=-2,y=-3\right)\\ -3=8\mathrm{....}\left(\text{False}\right)\\ B.y=x^2+1\\ \left(-3\right)={\left(-2\right)}^2+1\mathrm{....}\left(\text{For }x=-2,y=-3\right)\\ -3=5\mathrm{....}\left(\text{False}\right)\end{array}$

Similarly,

  $\begin{array}{c}C.y=-x^2+1\\ \left(-3\right)=-{\left(-2\right)}^2+1\mathrm{....}\left(\text{For }x=-2,y=-3\right)\\ -3=-3\mathrm{....}\left(\text{True}\right)\\ D.y=-x-1\\ \left(-3\right)=-\left(-2\right)-1\mathrm{....}\left(\text{For }x=-2,y=-3\right)\\ -3=1\mathrm{....}\left(\text{False}\right)\end{array}$

Since for $x=-2,y=-3$ the only function $y=-x^2+1$ satisfy the required result, so option (C) is correct.