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

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 =

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:

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 (-∞,∞).

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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:
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