on. provide a table of values and plot all possible points that 2) f(x)=-x^4 + 2x^2 - 2x - 2 4) f(x)=x^4 +…

Explanation:

Step1: Choose x - values

Let's choose (x=- 3,-2,-1,0,1,2,3)

Step2: Calculate corresponding y - values for (y = f(x)=-x^{4}+2x^{2}-2x - 2)

When (x=-3): [ \begin{align*} y&=-(-3)^{4}+2(-3)^{2}-2(-3)-2\ &=-81 + 18+6 - 2\ &=-59 \end{align*} ] When (x = - 2): [ \begin{align*} y&=-(-2)^{4}+2(-2)^{2}-2(-2)-2\ &=-16+8 + 4-2\ &=-6 \end{align*} ] When (x=-1): [ \begin{align*} y&=-(-1)^{4}+2(-1)^{2}-2(-1)-2\ &=-1 + 2+2-2\ &=1 \end{align*} ] When (x = 0): [ \begin{align*} y&=-0^{4}+2\times0^{2}-2\times0-2\ &=-2 \end{align*} ] When (x = 1): [ \begin{align*} y&=-1^{4}+2\times1^{2}-2\times1-2\ &=-1+2 - 2-2\ &=-3 \end{align*} ] When (x = 2): [ \begin{align*} y&=-2^{4}+2\times2^{2}-2\times2-2\ &=-16 + 8-4-2\ &=-14 \end{align*} ] When (x = 3): [ \begin{align*} y&=-3^{4}+2\times3^{2}-2\times3-2\ &=-81+18 - 6-2\ &=-71 \end{align*} ]

Step3: Create a table of values

(x)	(y=-x^{4}+2x^{2}-2x - 2)
(-3)	(-59)
(-2)	(-6)
(-1)	(1)
(0)	(-2)
(1)	(-3)
(2)	(-14)
(3)	(-71)

To plot the points, we use the (x) - values as the horizontal coordinates and the (y) - values as the vertical coordinates on the given (xy) - grid. For example, the point ((-3,-59)) is plotted by moving 3 units to the left of the origin along the (x) - axis and 59 units down along the (y) - axis. And so on for the other points ((-2,-6),(-1,1),(0,-2),(1,-3),(2,-14),(3,-71))

Answer:

The table of values is shown above and the points ((-3,-59),(-2,-6),(-1,1),(0,-2),(1,-3),(2,-14),(3,-71)) should be plotted on the given grid.