Exam 2: More on Functions

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 2 x + 4 } , g ( x ) = \sqrt { 25 x - 16 }$ Find (fg)(x) A) (2 x+4)(5 x-4) B) $( 5 x - 4 ) ( \sqrt { 2 x + 4 } )$ C) $( \sqrt { 2 x + 4 } ) ( \sqrt { 25 x - 16 } )$ D) (2 x+4)(25 x-16)

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$ - $f ( x ) = 9 | x | + 4 x$

Determine the domain and range of the function. - A) domain: [0,4]; range: [-3,0] B) domain: [-3,0]; range: [0,4] C) domain: [0,3]; range: $( - \infty , 4 ]$ D) domain: $( - \infty , 4 ]$ range: [0,3]

Write an equation for the piecewise function. -

Solve the problem. -The intensity of light from a light source varies inversely as the square of the distance from the source. Suppose the the intensity is 40 foot-candles at a distance of 10 feet. What will the intensity be at a distance of 23 feet? Round your answer to the tenths place.

Write an equation for the piecewise function. -

Graph the function. - A) B) C) D)

Find an equation of variation for the given situation. -y varies directly as x and inversely as z , and y=4 when x=2 and z=6 .

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= f(-x)+ 4

Solve. -A rectangular box with volume 400 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base. Express the cost the box as a function of x. A) $C ( x ) = 4 x + \frac { 3200 } { x ^ { 2 } }$ B) $C ( x ) = 3 x ^ { 2 } + \frac { 3200 } { x }$ C) $C ( x ) = 2 x ^ { 2 } + \frac { 3200 } { x }$ D) $C ( x ) = 3 x ^ { 2 } + \frac { 1600 } { x }$

Graph the function. - $g ( x ) = ( x + 2 ) ^ { 3 }$ A) B) C) D)

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$ Find (f+g)(x)

Solve. -A rectangle that is x feet wide is inscribed in a circle of radius 21 feet. Express the area of the rectangle as a function of x . A) B) C) D)

Find an equation of variation for the given situation. -y aries jointy as x and p and inverely as the square of s, and $y = \frac { 1 } { 2 }$ when x=1, p=1, and s=2 . A) $y = \frac { 4 x ^ { 2 } p } { s ^ { 2 } }$ B) $y = \frac { 2 x p } { s ^ { 2 } }$ C) $y = \frac { 6 x p ^ { 2 } } { s }$ D) $y = 7 x p s ^ { 2 }$

Graph the function. Use the graph to find any relative maxima or minima. -

Solve the problem. -The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet, What force would be required to keep the same car from skidding on a curve of radius 700 feet at 30 mph? Round your answer to the nearest pound of force?

Answer the question. -How can the graph of be obtained from the graph of A) Reflect it across the y-axis. Stretch it vertically by a factor of 1 . B) Reflect it across the x -axis. Stretch it vertically by a factor of 1 . C) Reflect it across the x-axis. Shrink it vertically by a factor of 0.1 . D) Reflect it across the y-axis. Shrink it vertically by a factor of 0.1 .

For the pair of functions, find the indicated sum, difference, product, or quotient. -f(x)=x+5, g(x)=x-4 Find (f+g)(-4) .

Solve. -A rectangular box with volume 517 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent The length of a side of the base in feet. Express the cost of the box as a function of x and then graph This function. From the graph find the value of x, to the nearest hundredth of a foot, which will Minimize the cost of the box.

For the pair of functions, find the indicated domain. - $f ( x ) = x ^ { 2 } - 36 , g ( x ) = 2 x + 3$ Find the domain of $g \text { of. }$ A) $\left( - \infty , - \frac { 3 } { 2 } \right) \cup \left( - \frac { 3 } { 2 } , \infty \right)$ B) $\left[ - \frac { 3 } { 2 } , \infty \right]$ C) (-6,6) D) $( - \infty , \infty )$