Question

Which of the following graphs represents the function f(x) = x3 − x2 − 10x − 8?

Answer 1

Graph the cubic using its end behavior and a few selected points.

Falls to the left and rises to the right

x

y

−

1

0

0

−

8

1

−

18

2

−

24

3

−

20

Answer 2

The cubic function is
`f(x)=x^3-x^2-10x-8`

Find the point at x=0,

Replace the variable x with 0 in f(x),

`f(0)=0^3-0^2-10(0)-8=-8`

Find the point at x=1,

Replace the variable x with 1 in f(x),

`f(1)=1^3-1^2-10(1)-8=1-1-10-8=-18 \\ y=-18`

Find the point at x=-1,

Replace the variable x with -1 in f(x):

`f(-1)=(-1)^3-(-1)^2-10(-1)-8\\ =-1-1+10-8=0\\ y=0`

Find the point at x=3,

REplace the variable x with 3 in f(x):

`f(3)=3^3-3^2-10*3-8=-20`

Similarly find few more points of this function:

f(-2)=0

f(2)=-24

f(5)=42

Now the cubic function
`f(x)=x^3-x^2-10x-8` using the following points

x: -5 -1 0 1 2 3 5

y: - 108 0 -8 -18 -24 -20 42

Using this points now graph the function,