91Ó°ÊÓ

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=2.5 x-4.25$$

Find the distance between the points. $$(-2,6),(3,-6)$$

Find the slope and \(y\) -intercept (if possible) of the equation of the line, Sketch the line. $$3 y+5=0$$

Find the slope and \(y\) -intercept (if possible) of the equation of the line, Sketch the line. $$7 x-6 y=30$$

Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(h(t)=t^{2}-2 t\) (a) \(h(2)\) (b) \(h(1.5)\) (c) \(h(x+2)\)

\(g\) 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 \(f.\) $$g(x)=2(x-7)^{2}$$

Evaluate the function for the indicated values. \(g(x)=-7[x+4]+6\) (a) \(g\left(\frac{1}{8}\right)\) (b) \(g(9)\) (c) \(g(-4)\) (d) \(g\left(\frac{3}{2}\right)\)

Use the given values of \(k\) and \(n\) to complete the table for the inverse variation model \(y=k x^{n} .\) Plot the points in a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|}\hline x & 2 & 4 & 6 & 8 & 10 \\\\\hline y=k / x^{n} & & & & & \\\\\hline\end{array}$$ $$k=10, n=2$$

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$(-16.8,12.3),(5.6,4.9)$$

Find (a) \(f \circ g\) and (b) \(g \circ f .\) Find the domain of each function and each composite function. $$f(x)=\sqrt[3]{x-5}, \quad g(x)=x^{3}+1$$