Question

2. Consider the function, f(x)=x^3+x^2-9x-9

Answer 1

The intercepts of the graph are:

x-axis interception: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$.

y-axis interception: $\left(0,\:-9\right)$.

See the graph of the function $f(x)=x^3+x^2-9x-9$  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.

• Determine the points

Replace these x-values in the given equation. For example:

When x=-4, we will have: $\left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21$.  Do this for the all x-values of your ranges.

See the results for this step in the attached table.

• Draw the graph

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: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$.

y-axis interception point (x=0) is: $\left(0,\:-9\right)$.

Learn more about intercepts of the graph here:

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