Pre Calculus Questions & Answers

Verifica che il grafico di \( y=\frac{1}{1-x} \) ha un asin- toto verticale di equazio- ne \( x=1 \)

Sketch the graph of each function. \( y=\frac{1}{4} \cdot\left(\frac{1}{3}\right)^{x-1}-1 \)

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. \[ h(x)=3^{x+2}-2 \] A. The graph of \( f(x)=3^{x} \) should be horizontally shifted 2 units to the left and vertically shifted 2 units upward. B. The graph of \( f(x)=3^{x} \) should be horizontally shifted 2 units to the left and correct answer below. vertically shifted 2 units downward. C. The graph of \( f(x)=3^{x} \) should be horizontally shifted 2 units to the right and vertically shifted 2 units downward. D. The graph of \( f(x)=3^{x} \) should be horizontally shifted 2 units to the right and to graph the function \( h(x)=3^{x+2}-2 \) ? Choose the vertically shifted 2 units upward.

MathJax Zoomed Expression \( \frac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}} \)

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 \( B=A \) ?