Problem 12
In Exercises \(9-12,\) use a graph to find the zeros of the function. $$f(x)=3-2^{x}$$
Problem 12
In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=1+\frac{1}{x^{2}}$$
Problem 12
In Exercises \(11-14,\) determine (a) the period, (b) the domain, (c) the range, and (d) draw the graph of the function. $$y=2 \sin (4 x+\pi)+3$$
Problem 12
In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=4 \cos t, \quad y=2 \sin t, \quad 0 \leq t \leq 2 \pi$$
Problem 12
In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(-\pi, 0)$$
Problem 12
In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=2^{3-x}$$
Problem 13
In Exercises \(13-24,\) find \(f^{-1}\) and verify that $$\left(f \circ f^{-1}\right)(x)=\left(f^{-1} \circ f\right)(x)=x$$ \(f(x)=2 x+3\)
Problem 13
In Exercises \(13-16,\) write the point-slope equation for the line through the point \(P\) with slope \(m .\) $$P(1,1), \quad m=1$$
Problem 13
In Exercises \(11-14,\) determine (a) the period, (b) the domain, (c) the range, and (d) draw the graph of the function. $$y=-3 \tan (3 x+\pi)+2$$
Problem 13
In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=4 \sin t, \quad y=2 \cos t, \quad 0 \leq t \leq \pi$$
