The intercepts of the graph are:
x-axis interception: [tex]\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)[/tex].
y-axis interception: [tex]\left(0,\:-9\right)[/tex].
See the graph of the function [tex]f(x)=x^3+x^2-9x-9[/tex] in the attached image.
Constructing a graph
For constructing a graph we have the following steps:
- Determine the range of values for x of your graph.
For this exercise, for example, we can define a range -4<x<4. In others words, the values of x will be in this interval.
Replace these x-values in the given equation. For example:
When x=-4, we will have: [tex]\left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21[/tex]. Do this for the all x-values of your ranges.
See the results for this step in the attached table.
Mark the points x and y that you found in the last step. After that, connect the dots to draw the graph.
The attached image shows the graph for the given function.
Find the x- and y-intercepts
The intercepts are points that crosses the axes of your plot. From your graph is possible to see:
x-axis interception points (y=f(x)=0) are: [tex]\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)[/tex].
y-axis interception point (x=0) is: [tex]\left(0,\:-9\right)[/tex].
Learn more about intercepts of the graph here:
https://brainly.com/question/4504979
