Algebra/Chapter 8/Exercises

A set of exercises related to concepts from Chapter 8.

This set contains 18 problems (0 Conceptual Questions + 18 Exercises + 0 Projects)

Exercises

Section 8.1

(★) 8.1 (Evaluating a Piecewise Function I) For the function f(x), find the following values.

(★) 8.2 (Evaluating a Piecewise Function II) For the function g(x), find the following values.

(★) 8.3 (Evaluating a Piecewise Function III) For the function h(x), find the following values.

(★) 8.4 (Evaluating a Piecewise Function IV) For the function i(x), find the following values.

(★) 8.5 (Evaluating a Piecewise Function V) For the function j(x), find the following values.

(★) 8.6 (Evaluating a Piecewise Function VI) For the function k(x), find the following values.

(★) 8.7 (Graphing Piecewise Functions) Graph the following piecewise functions.

(★) 8.8 (Domain and Range) Write the domain and range of the functions from Problem 8.7 in interval notation.

(★) 8.9 (Continuity) Determine if the following piecewise functions are continuous.

(★★) 8.10 (Cell Phones) A cellphone company offers two plans.

(★★) 8.11 (Continuity) Determine the value(s) of k which makes the following piecewise function continuous.

function:

$$f(x)={\begin{cases}3x+2,&{\text{if }}x<k\\2x-3,&{\text{if }}k\leq x\leq 8\end{cases}}$$

Section 8.2

(★★) 8.12 (Absolute Ratio) Simplify the following expression given that $x<0.$

${\frac {|x|}{x}}$

(★★) 8.13 (Range of Values I) If $24<x<39$, what is the value of the following expression?

$|x-24|+|x-39|$

(★★) 8.14 (Range of Values II) If $-12\leq x<12$, what is the value of the following expression?

$|x-14|+|x-12|+|x+12|+|x+14|$

(★★★) 8.15 (Range of Values III) If $-19\leq x\leq y\leq 4$, what is the value of the following expression?

$|x+19|+|x-y|+|y-4|$

(★★) 8.16 (Least Possible Absolute Value) If n is an integer, what is the smallest possible value of the following expression?

$|123-5n|$

(★★) *8.17 (The Triangle Inequality) For any triangle, the sum of the lengths of any two of its sides must be greater than or equal to the length of the third. This relation is represented as follows:

$|a+b|\leq |a|+|b|$

1. Use this relation to determine if a triangle with the side lengths of 6, 9, and 14 exists.
2. Use this relation to determine if a triangle with the side lengths of 5, 10, and 15 exists.
3. Outside of geometric applications, the above inequality also states that the absolute value of the sum of two numbers a and b are less than or equal to the sum of the absolute value of a and the absolute value of b. Prove that this relation is true.

Section 8.4

(★★★) 8.18 (GIF and LIF Equation) Find the range of values for x such that

⌊x⌈x⌉⌋ = 2000

Express your answer in interval notation.