Answer to Question #209905 in Discrete Mathematics for Sach

Question

Draw graphs of the following functions.

(a)

f: R—>R defined by f(x) = x

(b)

f: R—>R defined by f(x) = |x|

(c)

f: R—>R defined by f(x) = x + 1

(d)

f: R—>R defined by f(x) = – 3x+4

(e)

f: R—>R defined by f(x) = Floor(x)

(f)

f: R—>R defined by f(x) = Ceiling(x)

(g)

f: R—>R defined by f(x) = x2

(h)

f: R—>R defined by f(x) = x3

Answer 1

(a) $f:R\rightarrow R$ defined by $f(x) = x$

(b) $f:R\rightarrow R$ defined by $f(x) = |x|$

(c) $f:R\rightarrow R$ defined by $f(x) = x+1$

(d) $f:R\rightarrow R$ defined by $f(x) = -3x+4$

(e) $f:R\rightarrow R$ defined by $f(x) = Floor(x)$

The floor function is the function that takes as input a real number $x,$ and gives as output the greatest integer less than or equal to $x,$ denoted $Floor(x)$ or $\lfloor x \rfloor.$

(f) $f:R\rightarrow R$ defined by $f(x) = Ceiling(x)$

 The ceiling function is the function that takes as input a real number $x,$ and gives as output the least integer greater than or equal to $x,$ denoted $Ceiling(x)$ or $\lceil x\rceil.$

(g) $f:R\rightarrow R$ defined by $f(x) = x^2$

(h) $f:R\rightarrow R$ defined by $f(x) = x^3$