91Ó°ÊÓ

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)=|x|+4 $$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(=-\frac{2}{3},\) passing through \((6,-2)\)

In Exercises \(21-32,\) evaluate each function at the given values of the independent variable and simplify. $$g(x)=x^{2}+2 x+3$$ a. \(g(-1)\) b. \(g(x+5) \quad\) c. \(g(-x)\)

Find: a. \((f \circ g)(x)\) b. \(\left(g^{\circ} f\right)(x)\) c. \((f \circ g)(2)\) $$f(x)=x^{2}+2, g(x)=x^{2}-2$$

Find the midpoint of each line segment with the given endpoints. $$ (-3,-4) \text { and }(6,-8) $$

Find: a. \((f \circ g)(x)\) b. \(\left(g^{\circ} f\right)(x)\) c. \((f \circ g)(2)\) $$f(x)=x^{2}+1, g(x)=x^{2}-3$$

In Exercises \(21-32,\) evaluate each function at the given values of the independent variable and simplify. $$g(x)=x^{2}-10 x-3$$ a. \(g(-1)\) b. \(g(x+2) \quad\) c. \(g(-x)\)

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)=|x|+3 $$

Find the midpoint of each line segment with the given endpoints. $$(-2,-1) \text { and }(-8,6)$$

The functions in Exercises \(11-30\) are all one-to-one. For each function: a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$f(x)=\sqrt[3]{x}$$