Question

if ( f(x)=operatorname{int}(4 x) ), find:
(a) ( f(2.7) ) (b) ( f(2.4) ) (c) ( f(-3.6) )
(a) ( f(2.7)= ) (simplify your answer.)
(b) ( f(2.4)= ) (simplify your answer.)
(c) ( f(-3.6)= ) (simplify your answer.)

Explanation:

Step1: Calculate \(4x\) for each case

• For \(x = 2.7\), \(4x=4\times2.7 = 10.8\).
• For \(x = 2.4\), \(4x=4\times2.4=9.6\).
• For \(x=-3.6\), \(4x = 4\times(-3.6)=-14.4\).

Step2: Apply the int function

The int function (also known as the greatest - integer function or floor function) \(\text{int}(n)\) gives the greatest integer less than or equal to \(n\).

• For \(n = 10.8\), \(\text{int}(10.8)=10\).
• For \(n = 9.6\), \(\text{int}(9.6)=9\).
• For \(n=-14.4\), \(\text{int}(-14.4)=-15\) (since \(-15<-14.4\) and \(-14>-14.4\)).

Answer:

(a) \(10\)
(b) \(9\)
(c) \(-15\)