Exam 2: More on Functions

Determine the domain and range of the function. -

The graph of the function f is shown below. Match the function g with the correct graph. -

For the pair of functions, find the indicated domain. - $f ( x ) = 3 x - 2 , g ( x ) = \frac { 3 } { x + 7 }$ Find the domain of f+g A) $( - \infty , - 3 ) \text { or } ( - 3 , \infty )$ B) $( - \infty , \infty )$ C) $( 0 , \infty )$ D) $( - \infty , - 7 ) \text { or } ( - 7 , \infty )$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x - 4 , g ( x ) = - 4 x ^ { 2 } + 16 x - 4$ Find (fg)(3) A) -53 B) -8 C) -280 D) 56

The graph of the function f is shown below. Match the function g with the correct graph. - $g ( x ) = - \frac { 1 } { 2 } f ( x )$

Find the requested function value. - Find A) -16 B) -36 C) 324 D)

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). -g(x)=f(x-1) ;(4,14) A) (4,15) B) (3,14) C) (5,14) D) (4,13)

Write an equation for the piecewise function. -

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 3 \sqrt [ 3 ] { x }$

Solve. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 315 seconds are required to make a 5 -by- 7 enlargement, find the time required for a 6 -by- 10 enlargement.

Using the graph, determine any relative maxima or minima of the function and the intervals on which the function is increasing or decreasing. Round to three decimal places when necessary. - $f ( x ) = \frac { 1 } { 2 } x ^ { 3 } + \frac { 1 } { 2 } x ^ { 2 } - x + 1$

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

Answer the question. -How can the graph of $f ( x ) = - ( x - 1 ) ^ { 2 } + 6$ be obtained from the graph of $y = x ^ { 2 } ?$ A) Shift it horizontally 1 units to the left. Reflect it across the x -axis. Shift it 6 units up. B) Shift it horizontally 1 units to the right. Reflect it across the x -axis. Shift it 6 units up. C) Shift it horizontally 1 units to the right. Reflect it across the y-axis. Shift it 6 units up. D) Shift it horizontally 1 units to the right. Reflect it across the y-axis. Shift it 6 units down.

Solve. -At Allied Electronics, production has begun on the X-15 Computer Chip. The total cost function is given by C(x)=7 x+14 and the total profit function is given by $P ( x ) = - 0.3 x ^ { 2 } + 51 x - 14$ where x represents the number of boxes of computer chips produced. The total revenue function, R(x) , is such that R(x)=C(x)+P(x) . Find R(x) . A) $R ( x ) = 58 x + 0.3 x ^ { 2 }$ B) $R ( x ) = 58 x - 0.3 x ^ { 2 }$ C) $R ( x ) = 57 x - 0.6 x ^ { 2 }$ D) $R ( x ) = 60 x - 0.3 x ^ { 2 }$

Find an equation of variation for the given situation. - p varies directly as q , and p=1 when $q = \frac { 1 } { 3 } .$ A) $p = \frac { 1 } { 3 } q$ B) p=4 q C) p=3 q D) p=2 q

The graph of the function f is shown below. Match the function g with the correct graph. -g(x)= 2f(x)

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