Question

PLEASE HELP USING THE GRAPH BELOW SELECT ALL STATEMENTS THAT ARE TRUE

A. This is the graph of the greatest integer function

B. f(4.5)=5

C. This graph is one-to-one

D. f(0)=0

E. f(1.4)=1

Answer 1

A definitely has to be one because it's a fact and you need to know what it looks like. B isn't true because the greatest integer function rounds down values. C is also not correct because a one-to-one graph has one x-value for every y-value. This one doesn't. D has to be true because f[0] = 0 because the Greatest Integer Function requires it to be. And E is also correct because that's in the definition of a Greatest Integer Function. So, your answers are A, D and E.

Answer 2

Answer: The true options are,

A. This is the graph of the greatest integer function ,

D. f(0)=0

E. f(1.4)=1

Explanation:

By the given graph,

f(x) = 0 for 0 ≤ x < 1

f(x) = 1 for 1 ≤ x < 2,

f(x) = 2 for 2 ≤ x < 3,

f(x) = 3 for 3 ≤ x < 4,

.....so, on ....

That is, function f(x) gives integer value for an interval of values,

Since, For all real numbers, x, the greatest integer function gives the largest integer less than or equal to x.

Thus, given function f(x) is greatest integer function.

Also, greatest integer function is a many one function,

So, f(x) is not one to one,

Now, f(x) = 0 for 0 ≤ x < 1, f(x) = 1 for 1 ≤ x < 2

⇒ f(0) = 0 and f(1.4) = 1,

Therefore, option A, E and D are correct.