Lial - College Algebra 13th Edition - Chapter 3

Skip to main content

Ch. 2 - Graphs and Functions

Back

Lial 13th Edition

Ch. 2 - Graphs and Functions

Section 2.6

Problem 14

Determine the intervals of the domain over which each function is continuous.

Problem 15

Determine the intervals of the domain over which each function is continuous.

Problem 16

Determine the intervals of the domain over which each function is continuous.

Problem 19

For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).

$f (x) = {\begin{matrix} 2 + x & if x < - 4 \\ - x & if - 4 \leq x \leq 2 \\ 3 x & if x > 2 \end{matrix}$

Problem 21

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} x - 1 & if x \leq 3 \\ 2 & if x > 3 \end{matrix}$

Problem 22

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} 6 - x & if x \leq 3 \\ 3 & if x > 3 \end{matrix}$

Problem 23

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} 4 - x & if x < 2 \\ 1 + 2 x & if x \geq 2 \end{matrix}$

Problem 24

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} 2 x + 1 & if x \geq 0 \\ x & if x < 0 \end{matrix}$

Problem 25

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} - 3 & if x \leq 1 \\ - 1 & if x > 1 \end{matrix}$

Problem 28

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} - 2 x & if x < - 3 \\ 3 x - 1 & if - 3 \leq x \leq 2 \\ - 4 x & if x > 2 \end{matrix}$

Problem 29

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} - \frac{1}{2} x^{2} + 2 & if x \leq 2 \\ \frac{1}{2} x & if x > 2 \end{matrix}$

Problem 30

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} x^{3} + 5 & if x \leq 0 \\ - x^{2} & if x > 0 \end{matrix}$

Problem 35

Give a rule for each piecewise-defined function. Also give the domain and range.

Problem 37

Give a rule for each piecewise-defined function. Also give the domain and range.

Problem 39

Give a rule for each piecewise-defined function. Also give the domain and range.

Problem 41

Give a rule for each piecewise-defined function. Also give the domain and range.

Problem 44

Find the value of the function for the given value of x. ƒ(x)=[[0.5x]], for x=7

Problem 45

Find the value of the function for the given value of x. ƒ(x)=-[[-x]], for x=2.5

Problem 46

Find the value of the function for the given value of x. ƒ(x)=2-[[-x]], for x=3.7

Problem 47

Find the value of the function for the given value of x. ƒ(x)=[[x/4]], for x=7

Problem 48

Find the value of the function for the given value of x. ƒ(x)=[[3-(x/2)]], for x=1

Problem 49

Find the value of the function for the given value of x. ƒ(x)=[[x]], for x=(-π)

Problem 50

Find the value of the function for the given value of x. ƒ(x)=[[x]], for x=-√2

Problem 51

Find the value of the function for the given value of x.

$f (x) = {\begin{matrix} 5 & if 0 < x \leq 2 \\ 20 - 3 [[2 - 4 x]] & if x > 2 \end{matrix}, for x = 5.6$

Problem 52

Find the value of the function for the given value of x.

$f (x) = {\begin{matrix} 3 & if 0 < x \leq 4 \\ 10 - 2 [[5 - x]] & if x > 4, for \end{matrix}, for x = 6.2$

Problem 54

Graph each function. Give the domain and range. ƒ(x)=-[[x]]

Problem 55

Graph each function. Give the domain and range. ƒ(x)=[[2x]]

Problem 56

Graph each function. Give the domain and range. g(x)=[[2x-1]]

Section 2.7

Problem 17

Graph each function. See Examples 1 and 2. ƒ(x)=3|x|

Problem 19

Graph each function. See Examples 1 and 2. ƒ(x)=2/3|x|