Exam 2: More on Functions

Solve. -A rectangle that is x feet wide is inscribed in a circle of radius 20 feet. Express the area of the rectangle as a function of x. Graph the function and from the graph determine the value of x, to the Nearest tenth of a foot, which will maximize the area of the rectangle.

Determine whether the given function is even, odd, or neither even nor odd. - A) Neither B) Even C) Odd

Find the point that is symmetric to the given point with respect to the requested axis. -Symmetric with respect to the y-axis (1.5, -1.75)

For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$ - $f ( x ) = \frac { x - 19 } { x + 3 }$ A) $\frac { 23 } { ( x + 3 ) ( x - 3 ) }$ в) $\frac { 22 ( x + h + 3 ) } { ( x + 3 ) }$ C) $\frac { 22 } { ( x + h + 3 ) ( x + 3 ) }$ D) $- \frac { 22 } { x ( x + 3 ) }$

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. -y=|20 x|

Determine the domain and range of the function. -

Solve the problem. -The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 35 miles per hour in 40 minutes, how fast must it travel to cover the same distance in 50 minutes?

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=2-9 x, g(x)=-5 x+9 Find (f+g)(x) .

Answer the question. -How can the graph of $f ( x ) = ( x - 2 ) ^ { 2 } - 7$ be obtained from the graph of $y = x ^ { 2 } ?$ A) Shift it 2 units horizontally to the right. Shift it vertically 7 units downward. B) Shift it 2 units horizontally to the left. Shift it vertically 7 units downward. C) Shift it 2 units horizontally to the left. Shift it vertically 7 units upward. D) Shift it 7 units horizontally to the right. Shift it vertically 2 units downward.

Write an equation for a function that has a graph with the given characteristics. -The shape of $y = x ^ { 2 }$ but upside-down and vertically stretched by a factor of 6 .

round answer to the nearest hour Find an equation of variation for the given situation. -r varies directly as s , and r=0.3333 when s=1 .

Solve the problem. -The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If $\mathrm { V } = 392.0 \mathrm { in. } ^ { 3 }$ when $\mathrm { T } = 420 ^ { \circ }$ and $\mathrm { P } = 15 \mathrm { lb } / \mathrm { in } ^ { 2 }$ what is the volume when $\mathrm { T } = 200 ^ { \circ }$ and $\mathrm { P } = 15 \mathrm { lb } / \operatorname { in } ^ { 2 } ?$

Write an equation for the piecewise function. -

Solve. -A rectangle that is x feet wide is inscribed in a circle of radius 32 feet. Express the area of the rectangle as a function of x. Graph the function and from the graph determine the value of x, to the Nearest tenth of a foot, which will maximize the area of the rectangle.

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

Answer the question. -How can the graph of f(x)=-10|x| be obtained from the graph of y=|x| ?

Solve. -Elissa sells two breeds of dogs, Alaskan Malamutes and Great Pyrenees. She has 108 feet of fencing to enclose two adjacent rectangular dog kennels, one for each breed. An existing fence is to form One side of the kennels, as in the drawing below. Suppose the total length of the two kennels is x Feet. Express the total area of the two kennels as a function of x. Graph the function and from the Graph determine the value of x that will yield the maximum area. A) $54 \frac { 1 } { 2 } \text { feet }$ B) 54 feet C) 56 feet D) 53 feet

Write an equation for the piecewise function. -

The given point is on the graph of y = f(x). Find a point on the graph of y = g(x). - g(x)=3 f(x) ;(2,4) A) (5,2) B) (2,6) C) (6,4) D) (2,12)

A graph of y = f(x) follows. No formula for f is given. Graph the given equation. -y= f(2x)