Exam 2: Functions

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

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line. - $y = \frac { 1 } { x }$ Down 5 , right 6

Solve the problem. -The accompanying figure shows the graph of $y = - x ^ { 2 }$ shifted to a new position. Write the equation for the new graph.

Simplify the expression. - $e ^ { \ln 11 x - \ln 3 }$

Consider the function y Can x be 0? -What is the domain of the function $y = \sqrt { 1 - \frac { 1 } { x } }$ ?

Find the formula for the function. -A point P in the fourth quadrant lies on the graph of the function f(x) $f ( x ) = - x ^ { 2 }$ . Express the slope of the line joining P to the origin as a function of x.

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y = - x ^ { 2 } / 5$

Match the equation with its graph. - $y=5^{x}$

Graph the function. - $f(x)=-3^{-x}-5$

Simplify the expression. - $\log _ { 9 } \frac { 1 } { 81 }$

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. - $f \circ f$

Simplify the expression. - $\log _ { e } e ^ { | x - 19 | }$

State the domain and range of the function. - $f ( x ) = e ^ { - x } + 1$

Find the inverse of the function. - $f ( x ) = 5 x ^ { 3 } + 6$

Solve the problem. -How long will it take for prices in the economy to double at a 12% annual inflation rate? Round the answer to the nearest hundredth.

Graph the function. - $\text { Graph the function } f ( x ) = 2 \cos ^ { 3 } x \text {. }$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 32 ^ { 4 } } { 4 ^ { 4 } }$

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

Find the function value. - $\sin ^ { 2 } \frac { \pi } { 12 }$

Solve the problem. -Graph the functions $f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt { 5 - x }$ together with their sum, product, two differences, and two quotients.