91Ó°ÊÓ

Finding the Slope of a Line Through Two Points, plot the points and find the slope of the line passing through the pair of points. $$(0,-10),(-4,0)$$

Finding Compositions of Functions, find (a) \(f \circ g,(\) b) \(g \circ f,\) and \((\mathbf{c}) g \circ g .\) $$f(x)=3 x+5, \quad g(x)=5-x$$

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. \(y^{2}=x+1\)

Plotting, Distance, and Midpoint, (a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ (1,12),(6,0) $$

Identifying a Parent Function In Exercises \(21-46\) , \(g\) 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 $$g(x)=(x+3)^{3}-10$$

Determine the intervals on which the function is increasing, decreasing, or constant. \(f(x)=x^{2}-4 x\)

Evaluating a Function In Exercises \(21-32\) , evaluate (if possible) the function at each specified value of the independent variable and simplify. $$ f(x)=\left\\{\begin{array}{ll}{4-5 x,} & {x \leq-2} \\ {0,} & {-2 < x < 2} \\\ {x^{2}+1,} & {x \geq 2}\end{array}\right. $$ $$ \begin{array}{ll}{\text { (a) } f(-3)} & {\text { (b) } f(4)}\end{array} \quad(\text { c) } f(-1) $$

Determine the intervals on which the function is increasing, decreasing, or constant. \(f(x)=x^{3}-3 x^{2}+2\)

Identifying a Parent Function In Exercises \(21-46\) , \(g\) 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 $$g(x)=3(x-2)^{3}$$

Finding the Slope of a Line Through Two Points, plot the points and find the slope of the line passing through the pair of points. $$(4.8,3.1),(-5.2,1.6)$$