Exam 1: Functions, Graphs, and Limits

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 4 ^ { - } } f ( x )$ where $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & \text { if } x \leq 4 \\x + 8 & \text { if } x > 4\end{array} \right.$

Find the slope (if possible) of the line that passes through the given pair of points. (11, 6) and (5, 4).

Find the slope of the line whose equation is given. 3x + 5y = -7

Find the slope (if possible) of the line that passes through the given pair of points. (5, 0) and (3, 4)

Find the composite function $f ( g ( x ) )$ $f ( u ) = \frac { 1 } { u } , g ( x ) = x + 3$

Find an equation of the line parallel to the line y-axis and through the point (3, 9).

Find the slope of the line whose equation is given. 3x - 5y = 9.

Find the composite function $f ( g ( x ) )$ . $f ( u ) = \frac { 1 } { u } - u$ , g(x) = 2x - 3

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$

Find functions h(x) and g(u) such that $f ( x ) = g ( h ( x ) )$ : $f ( x ) = \frac { 5 } { \sqrt { x + 4 } } + 3 \sqrt { x + 4 }$

Find the slope (if possible) of the line that passes through the given pair of points. (-1, 5) and (7, 2)

Find the slope and y-intercept of the line whose equation is given. $\frac { x } { 3 } + \frac { y } { 5 } = 1$

Find an equation of the line parallel to the line y-axis and through the point (9, 3).

Compute the indicated value of the given function. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } - 5 & \text { if } x < 1 \\4 & \text { if } x = 1 \\7 - 8 x & \text { if } x > 1\end{aligned} \right.$ ; f (2)

Compute the indicated values of the given function. f (x) = x - 3 + | x - 5| ; f (-4), f (-3), f (-2).

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ . If the limiting value is infinite indicate whether it is + $\infty$ or - $\infty$ . $f ( x ) = \frac { 1 - 4 x ^ { 3 } } { 5 x ^ { 3 } - 9 x - 3 }$

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists.

Find the points of intersection (if any) of the given pair of curves. y = 7x - 4 and y = 3x - 5

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$

Determine the domain of the given function. $f ( x ) = \sqrt { x - 3 }$