91Ó°ÊÓ

\(\mathrm{G}\) is related to one of the parent functions described in Section 1.6. (a) Identify the parent function \(f\). (b) Describe the sequence of transformations from \(f\) to \(g\). (c) Sketch the graph of \(g\). (d) Use function notation to write \(g\) in terms of \(f\). $$ g(x)=\sqrt{3 x+1} $$

Identify any intercepts and test for symmetry. Then sketch the graph of the equation. $$ x=y^{2}-1 $$

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$ y=3-\frac{1}{2} x $$

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{x-3}{x+2} $$

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{6 x+4}{4 x+5} $$

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=3 x+5 $$

The cost of sending an overnight package from Los Angeles to Miami is $$\$ 23.40$$ for a package weighing up to but not including 1 pound and $$\$ 3.75$$ for each additional pound or portion of a pound. A model for the total cost \(C\) (in dollars) of sending the package is \(C=23.40+3.75 \llbracket x \rrbracket, x>0,\) where \(x\) is the weight in pounds. (a) Sketch a graph of the model. (b) Determine the cost of sending a package that weighs 9.25 pounds.

During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise- defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross- sectional area. If \(\\# 28\) copper wire (which has a diameter of 0.0126 inch) has a resistance of 66.17 ohms per thousand feet, what length of \(\\# 28\) copper wire will produce a resistance of 33.5 ohms?

Plot the points (2,1), \((-3,5),\) and (7,-3) on a rectangular coordinate system. Then change the sign of the \(x\) -coordinate of each point and plot the three new points on the same rectangular coordinate system. Make a conjecture about the location of a point when each of the following occurs. (a) The sign of the \(x\) -coordinate is changed. (b) The sign of the \(y\) -coordinate is changed. (c) The signs of both the \(x\) - and \(y\) -coordinates are changed.