1. A continuacion, se presentan diferentes funciones, determina si se trata de una funcion logaritmica o una exponencial y unelas con su grafica correspondiente. a. \( f(x)=\log _{7}(x-4)+1 \) b. \( g(x)=5(3)^{x} \) c. \( h(x)=\ln (x-3) \) d. \( f(x)=e^{2 x} \) e. \( k(x)=\log _{90}\left(x^{2}\right) \) f. \( f(x)=2^{x}+3 \) g. \( m(x)=\log _{3}(x+1) \) h. \( n(x)=7(0.8)^{x} \) i. \( o(x)=\log _{9}(2 x+7) \) i. \( p(x)=0.5(4)^{x} \)

d) \( f(x)=\sqrt{x}-x+2, A(1 \mid f(1)) \)

Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing. \( f(x)=3 x^{2}+6 x-45 \) Select the correct choice below and fill in the answer box within your choice. (Type an integer or a fraction.) A. The parabla opens downward and has a maximum value of B. The parabola opens upward and has a minimum value of (c) What is the range of \( f(x) \) ? The range of \( f(x) \) is \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) (d) On what interval is the function increasing? The function is increasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

(a) The graph of \( y=f(x) \) is shown. Translate it to get the graph of \( y=f(x-5) \). (b) The graph of \( y=g(x) \) is shown. Translate it to get the graph of \( y=g(x)-2 \).

Restrict the domain of \( f(x) \) so that \( f \) is one-to-one. Then find \( f^{-1}(x) \). \( f(x)=-2-x^{2} \)

Below is the graph of \( y=\sqrt{x} \) Translate it to make it the graph of \( y=\sqrt{x+4}-2 \).