Answer:
The sketch of the graph is given below.
Explanation:
To sketch the curve of the function ( f(x) = (x + 3)(x + 2)(x - 1) ) and identify the points of intersection with the coordinate axis, we can follow these steps:
Step 1: Find the x-intercepts
The x-intercepts occur where the curve crosses the x-axis, so we set ( f(x) = 0 ) and solve for x:
[ (x + 3)(x + 2)(x - 1) = 0 ]
This gives us the x-coordinates of the points where the curve intersects the x-axis.
Step 2: Find the y-intercept
The y-intercept occurs where the curve crosses the y-axis, which is when ( x = 0 ). We can find the y-coordinate by evaluating ( f(0) ).
Step 3: Sketch the curve
Using the x and y-intercepts, along with additional points if needed, we can sketch the curve of the function ( f(x) ).
Thus, the sketch of the graph is given above.