Graph the following equation by hand. Then find the x-intercept and determine where the graph is increasing and where it is decreasing

Question

Graph the following equation by hand. Then find the x-intercept and determine where the graph is increasing and where it is decreasing.

 

y = [ 2x - 5] 

 

the x - intercept of the graph is x = 

Answer 1

Square brackets traditionally meant the greatest integer function, now called the floor function.

 

So y = [2x - 5] = Floor(2x - 5) = ⌊2x - 5⌋ where there are little hooks on the bottom of the container glyphs.

 

Here's a GeoGebra graph:

http://www.dropbox.com/s/p60wrjb07r9dhyf/sks23cu14012801.png

 

Find the x-intercept and determine where the graph is increasing and where it is decreasing.

 

The x-intercept is a line segment: y = 0 for 2.5 ≤ x < 3.

 

From Wolfram, "A function f(x) increases on an interval I if f(b) ≥ f(a) for all b > a, where a,b in I."

 

So y = Floor(2x - 5) is increasing on the interval (-∞,∞).

 

=====

 

If the function was meant to be the absolute value function,

 

y = |2x - 5|

 

y = 2 | x - 5/2 |

 

which is y = |x| stretched by 2 times in the y-direction and shifted right by 5/2.

 

The graph is increasing on the interval (5/2, ∞) and

decreasing on the interval (-∞, 5/2).

 

The x-intercept is x = 5/2, the location of the vertex.

 

Here's a graph:

http://www.dropbox.com/s/z6gltc0jihdqi9r/sks23cu14012901.png

Answer 2

 Y = l 2X - 5 l 

 

 2X - 5 = 0   x = 5/2

 

 Locate ( 2, 0) connect ( 2, 0) to ( 0,5 ) , and ( 2,0) to ( 3 , 10) .

 

From ( -∞, 2) decreasing

 

From ( 2 , +∞ ) increasing