195k views
0 votes
Given the function f(x) = (x + 3)(x + 2)(x - 1), sketch the curve y = f(x), showing the points of intersection with the coordinate axis.

User Sangwoo
by
7.0k points

1 Answer

1 vote

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.

Given the function f(x) = (x + 3)(x + 2)(x - 1), sketch the curve y = f(x), showing-example-1
User Victor Perov
by
7.5k points