Problem 8
In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=x^{2}+5 x$$
Problem 8
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?
$$x=\left(\sec ^{2} t\right)-1, \quad y=\tan t, \quad-\pi / 2
Problem 8
In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=-\sqrt{-x}$$
Problem 8
In Exercises \(5-8,\) rewrite the exponential expression to have the indicated base. \((1 / 27)^{x}, \quad\) base 3
Problem 9
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? $$x=\cos t, \quad y=\sin t, \quad 0 \leq t \leq \pi$$
Problem 9
In Exercises 9 and \(10,\) find all the trigonometric values of \(\theta\) with the given conditions. $$\cos \theta=-\frac{15}{17}, \quad \sin \theta>0$$
Problem 9
In Exercises \(9-12,\) use a graph to find the zeros of the function. $$f(x)=2^{x}-5$$
Problem 9
In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=\frac{1}{x-2}$$
Problem 9
In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(3,2)$$
Problem 9
In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=x^{3}-4 x+6$$
