Graph using a table of values; make sure to use both positive and negative values for x.
Graph:
Relative Maximum: x ≈-1.8 Relative Minimum: x ≈ 1.1 Domain: {all real numbers} Range: {all real numbers}
Practice makes perfect
Let's make a table of values to graph the given function. When you are making a table of values, make sure to use a variety of points, including negative and positive values.
x
x^3+x^2-6x-3
f(x)=x^3+x^2-6x-3
- 3
( - 3)^3+( - 3)^2-6( - 3)-3
-3
- 2
( - 2)^3+( - 2)^2-6( - 2)-3
5
- 1
( - 1)^3+( - 1)^2-6( - 1)-3
3
0
0^3+ 0^2-6( 0)-3
- 3
1
1^3+ 1^2-6( 1)-3
- 7
2
2^3+ 2^2-6( 2)-3
- 3
We will now plot the obtained points and connect them with a smooth curve. Consider also that this is an odd-degreepolynomial with a positive leading coefficient. This tells us about the end behavior of the function.
&f(x) → - ∞ as x → - ∞
&f(x) → + ∞ as x → + ∞
Let's draw the function!
The value of f(x) at x=-1.8 is greater than the surrounding points, and the value of f(x) at x=1.1 is less than the surrounding points. Therefore, there must be a relative maximum near x=-1.8, and a relative minimum near x=1.1
Unless specific restrictions have been stated, the domain of polynomial functions is always all real numbers. The y-coordinates on the left of the graph will continue in the direction of the arrow and likewise on the right of the graph. The range is unrestricted and therefore is all real numbers.
Domain: & {all real numbers }
Range: & {all real numbers }
