Answer to Question #239087 in Calculus for Kathy

Question

Question 6

Classify each of the following functions as algebraic or transcendental.

a) 𝑓(𝑥) = tan(8𝑥)

b) 𝑓(𝑥) = √𝑥5+3 9𝑥+5

c) 𝑓(𝑥) = 9𝑥

d) 𝑓(𝑥) = 1+𝑥

A company that operates for 18 hours a day has introduced a new daily wage system that incorporates variable hourly rate to encourage longer shifts. The company pays $10 for first hour or any part of the first hour. Afterwards, company pays additional 2% per hour for each hour or part of each additional hour. Write a piece-wise function that shows the salary as a function of hours. Also sketch a graph of this function.

Question 8

Describe how the function 𝑓(𝑥) = −(𝑥 + 1)2 − 4 can be graphed using the graph of 𝑦 = 𝑥2 and a sequence of transformations.

Answer 1

$1. \text{ A transcendental function is an analytic function that does not satisfy a polynomial}\\ \text{equation while In mathematics, an algebraic function is a function that can be defined}\\ \text{ as the root of a polynomial equation. The function a is}\text{ transcedental while the functions}\\\text{ b, c, d are algebraic }\\ 2. \text{The piecewise function can be given by }\\ f(x) = 10 \text{ if $0 < x \leq 1 $}\\ f(x) = \frac{2}{100}.10(x-1)+10 \text{ if 1$\leq x \leq 18$}\\ \implies f(x) = \begin{cases} 10 \text{ if 0 < x $\leq$ 1 }\\ \frac{2x+98}{10} \text{ if $1< x \leq 18$} \end{cases}\\ 3. \text{ First the function $y = x^2$ undergoes reflection by multiplying it by -1, it is then }\\ \text{shifted 1 unit to the right, and it is shifted 4 units downward to get}\\ y = -(x+1)^2 -4\\ \text{The transformations can be represented graphically in the following images}\\$