# SKETCH A GRAPH FROM A VERBAL DESCRIPTION

Use the information below to sketch a graph of the polynomial function y  =  f(x).

* f(x) is positive on the intervals (-2, -1) and (1, 2).

* f(x) is negative on the intervals (-, -2), (-1, 1) and (2, ).

* f(x) is increasing on the intervals (-, -1.5) and (0, 1.5).

* f(x) is decreasing on the intervals (-1.5, 0) and (1.5, )

Step 1 :

Using the x-values in positive and negative intervals, we can draw vertical lines parallel to y-axis as shown below.

Step 2 :

The x-intercepts of the graph are

(-2, 0), (-1, 0), (1, 0) and (2, 0)

That is, the graph has to intersect x-axis at the above points.

Step 3 :

f(x) is positive on the intervals (-2, -1) and (1, 2).

So, the graph should be above the x-axis on the intervals

(-2, -1) and (1, 2).

Step 4 :

f(x) is negative on the intervals (-, -2), (-1, 1) and (2, ).

So, the graph should be below the x-axis on the intervals

(-, -2), (-1, 1) and (2, )

Step 5 :

f(x) is increasing on the intervals (-, -1.5) and (0, 1.5).

When we look at the graph from left to right, the graph should be upward on the intervals

(-, -1.5) and (0, 1.5)

Step 6 :

f(x) is decreasing on the intervals (-1.5, 0) and (1.5, )

When we look at the graph from left to right, the graph should be downward on the intervals

(-1.5, 0) and (1.5, )

Try Yourself :

Use the information below to sketch a graph of the polynomial function y  =  f(x).

* f(x) is positive on the intervals (-4, -2) and (2, 4).

* f(x) is negative on the intervals (-, -4), (-2, 2) and (4, ).

* f(x) is increasing on the intervals (-, -3) and (0, 3).

* f(x) is decreasing on the intervals (-3, 0) and (3, ).

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