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 =

Tutors, sign in to answer this question.

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 (-∞,∞).

=====

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:

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Alain F.

Native speaker for French and Master in Science Grad for Math!

$13.75 per 15 min

View Profile >

Kia R.

Learning English Can Be Fun....Let's Do It Together

$10 per 15 min

View Profile >

Mark A.

Improve your English based on your profession, schedule, and needs.

$11.25 per 15 min

View Profile >