Question

Graph the function y = |1.6x – 2| – 3.2. Over which interval is the function increasing?

Answer 1

You are to graph   y = |1.6x – 2| – 3.2.  I trust you know that the graph of y=|x| is v-shaped, opening up, with vertex at (0,0).

Let's rewrite y = |1.6x – 2| – 3.2 by factoring 1.6 out of  |1.6x - 2|:

                     y = 1.6*|x – 2/1.6| – 3.2

This tells us that the vertex of   y = |1.6x – 2| – 3.2   is at (2/1.6,  -3.2).  If you need an explanation of why this is, please ask.

Plot the vertex at (1.25, -3.2).
Find the y-intercept:  Let x = 0 in  y = |1.6x – 2| – 3.2 and find y:

                                                      y = 2-3.2 = -1.2

The y-intercept is located at 0, -1.2)

Plot this y-intercept.

Now draw a straight line from the vertex to this y-intercept.  Reflect that line across the y-axis to obtain the other half of the graph.

Answer 2

Answer:

The interval over which the function is increasing is:

                (1.25,∞)

Step-by-step explanation:

We are given a modulus function by:

        $y=|1.6x-2|-3.2$

From the graph of the function we see that the function is first decreasing in the interval (-∞,1.25) and then it increases continuously in the interval (1.25,∞) and goes to infinity.

     Hence, the answer is:

                   (1.25, ∞)