Exam 2: Functions

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. - $\mathrm { g } ^ { 2 }$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\tan x = 1 , \quad x$ in $\left[ \pi , \frac { 3 \pi } { 2 } \right]$

Determine whether or not the graph is a graph of a function of x. -

Determine if the function is even, odd, or neither. - $f ( x ) = 4 x ^ { 2 } + 2$

Provide an appropriate response. -Graph the functions $f ( x ) = \frac { x } { 2 }$ and $g ( x ) = 1 + \frac { 4 } { x }$ together to identify the values of $x$ for which $\frac { x } { 2 } > 1 + \frac { 4 } { x }$ . Confirm your findings algebraically.

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = x ^ { 2 } - 1 \quad$ stretched horizontally by a factor of 4

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\cos \left( \frac { \pi } { 4 } \right)$

Find a formula for the function graphed. -

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = 1 + \frac { 1 } { x ^ { 2 } } \quad$ compressed horizontally by a factor of 3

Graph the function. - $y=\sqrt{2 x-6}$

Simplify the expression. - $\ln \left( e ^ { 10 } \ln x \right)$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $3 ^ { 4 } \cdot 3 ^ { - 9 }$

Find the requested information using the law of cosines and/or the law of sines. Round to three decimal places. -A triangle has sides $a = 3$ and $b = 5$ and angle $C = 50 ^ { \circ }$ . Find the length of side $c$ .

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=(-x)^{3 / 2}$

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\sqrt [ 8 ] { 625 ^ { 2 } }$

For $f ( x ) = A \sin \left( \frac { 2 \pi } { B } ( x - C ) \right) + D$ identify either A, B, C, or D as ind icated for the sine function. Find A. - $y = - 2 \sin ( - \theta - \pi ) \quad$ Find $B$ .

Determine if the function is even, odd, or neither. -f(x) = 3

Graph the function. - $y=(x-4)^{2 / 3}$

Simplify the expression. - $\mathrm { e } ^ { \ln 6.0 }$