Exam 2: Functions and Graphs

In exercise physiology, aerobic power P is defined in terms of maximum oxygen intake. For altitudes up to 1,800 meters, aerobic power is optimal-that is, 100%. Beyond 1,800 meters, P decreases linearly from the maximum of 100% to a value near 40% at 5,000 meters. Estimate aerobic power at the altitude of 2,400 meters.

Find a formula that expresses the fact that P(x, y) is a distance 2 away from the origin.

Find the domain of $f$ . $f ( x ) = \frac { 8 } { 6 x ^ { 2 } + 18 x - 108 }$

Simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } \text {, if } h \neq 0$ for $f ( x ) = x ^ { 2 } + 4$

Find $( f \circ g ) ( x )$ . $f ( x ) = x ^ { 2 } - 4 x \text {, and } g ( x ) = \sqrt { x + 9 }$

Find $( f + g ) ( 3 )$ $f ( x ) = 8 x + 2$ , and $g ( x ) = x ^ { 2 }$

Find a composite function form for y if: $y = 4 + \sqrt { x ^ { 2 } + 3 }$

The volume of a conical pile of sand is increasing at a rate of $576 \pi$ ft ³ /min, and the height of the pile always equals the radius r of the base. Express r as a function of time t (in minutes), assuming that r = 0 when t = 0.

Find the distance d (A, B) between the points A (1, - 1) and B (8, 1).

Sketch the graph of the function. $f ( x ) = 3 x ^ { 2 } - 6 x - 5$

Several values of two functions T and S are listed in the following tables: t 0 1 2 3 T(t) 2 3 1 0 X 0 1 2 3 S(x) 1 0 3 2 Find: $( S \circ S ) ( 3 )$

Find an equation of the line shown in the figure.

Find the domain of $f g$ . $f ( x ) = \frac { 3 x } { x - 5 } , \text { and } g ( x ) = \frac { x } { x + 1 }$

Let y = f (x) be a function with domain D = [ -10, -9 ] and range R = [ -10, -7 ]. Find the domain D and range R for the function $y = | f ( x ) |$

Find the domain of $\text { f/g }$ . $f ( x ) = \sqrt { x + 7 } , \text { and } g ( x ) = \sqrt { x + 7 }$

If the point P (3, 1) is on the graph of a function f, find the corresponding point on the graph of the function $y = - 9 f ( x - 2 ) + 1$

Find $( g \circ f ) ( x )$ $f ( x ) = 6 x - 7$ , $g ( x ) = 4 x ^ { 2 } - x + 2$

Find the distance d (A, B) between the points A (6, 6) and B (6, - 4).

Find $( f / g ) ( 5 )$ . $f ( x ) = - x ^ { 2 }$ , and $g ( x ) = 6 x - 2$

An object is projected vertically upward with an initial velocity of $\mathcal { v } _ { 0 }$ ft/sec, and its distance $s ( t )$ in feet above the ground after $t$ seconds is given by the formula $s ( t ) = - 16 t ^ { 2 } + v _ { 0 } t$ . If the object hits the ground after $15$ seconds, find its initial velocity $\mathcal { v } _ { 0 }$ in ft/sec.