05) Um fabricante pode produzir calcados ao custo de \( R \$ 20,00 \) o par. Estima-se que, se cada par for vendido por \( x \) reais, o fabricante venderá por mês \( 80-x(0 \leq x \leq 80) \) pares de sapatos. Assim, o lucro mensal do fabricante é uma função do preço de venda. Qual deve ser o preço de venda, de modo que o lucro mensal seja máximo?

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{\mathrm{x}^{4}-3 \mathrm{x}^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is (Type an integer or decimal rounded to two decimal places as needed.)

If \( (-1,8) \) is a point on the graph of \( y=f(x) \), which of the following must be on the graph of \( y=f(-x) \) ? \( (8,1) \) \( (-1,-8) \) Choose the correct answer below. \( (1,8) \) \( (-8,-1) \)

Clearly indicate all intercepts with the axes as well as the QUESTION 7 Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : 7.1 Write the equations of the asymptotes of \( k \). 7.2 Give the range of \( k \). 7.3 Give the domain of \( k \).

122. Постройте график функции \( y=-x^{2}+2 x+8 \) и найдите, ис- пользуя график: а) значение функции при \( x=2,5 ;-0,5 ;-3 ; \) б) значения аргумента, при которых \( y=6 ; 0 ;-2 \); в) нули функции и промежутки знакопостоянства; г) промежутки возрастания и убывания функции, область зна- чений функции.

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{x^{4}-3 x^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is 2 . (Type an integer or decimal rounded to two decimal placels as needed.) (c) What is \( d \) if \( x=1 \) ? If \( x=1 \), the distance \( d \) is \( \square \). (Type an integer or decimal rounded to two decimal places as needed.)