Pre Calculus Questions & Answers

A. The graph of \( f(x)=3^{x} \) should be shifted 6 units downward. B. The graph of \( f(x)=3^{x} \) should be shifted 6 units to the left. C. The graph of \( f(x)=3^{x} \) should be shifted 6 units upward. D. The graph of \( f(x)=3^{x} \) should be shifted 6 units to the right. Graph \( g(x)=3^{x+6} \) and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line.

Begin by graphing \( f(x)=3^{x} \). Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x+6} \) Which transformation is needed to graph the function \( g(x)=3^{x+6} \) ? Choose the correct answer below. A. The graph of \( f(x)=3^{x} \) should be shifted 6 units downward. The graph of \( f(x)=3^{x} \) should be shifted 6 units to the left. C. The graph of \( f(x)=3^{x} \) should be shifted 6 units upward. D. The graph of \( f(x)=3^{x} \) should be shifted 6 units to the right.

Solve \& Graph (1) \( f(x)=2^{1+3 x} \) (2) \( f(x)=2^{1-3 x} \) (3) \( f(x)=3^{2-2 x} \) d) \( f(x)=3^{2+2 x} \)

Solve \& Graph (1) \( f(x)=2^{1+3 x} \) (2) \( f(x)=2^{1-3 x} \) (3) \( f(x)=3^{2-2 x} \) d) \( f(x)=3^{2+2 x} \)

Solve g Graph (1) \( f(x)=2^{1+3 x} \) (2) \( f(x)=2^{1-3 x} \) (3) \( f(x)=3^{2-2 x} \) d) \( f(x)=3^{2+2 x} \)

Exercice 2 On considère les ensembles \( A=\left\{\frac{1}{\sqrt{x^{2}+1}} / x \in \mathbb{R}\right\} \) et \( B=\left\{\frac{1}{\sqrt{x^{2}+1}+1} / x \in \mathbb{R}\right\} \) Montrer que \( B \subset A \). A-t-on \( B=A \) ?

Given the following exponential function, identify whether the change represe percentage rate of increase or decrease. \[ y=990(1.922)^{x} \]

The domain of the function \( f(x) \) is \( [5,12] \) and the range is \( [-11,19] \). Using interval find the domain and range of \( g(x)=-f(x) \).

1) Let \( z e t \) find \( z^{3} \) in polar form.

Graticar lafunción \( y=f(x)=3 x^{2}-5 x+2 \)