Exam 11: Functions

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = ( x - 7 ) ^ { 2 }$

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = x ^ { 2 } + 14 x + 45 , g ( x ) = x + 9$ Find $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$ .

For the functions f(x) and g(x), evaluate the indicated function. -Find $( f + g ) ( - 2 )$ when $f ( x ) = 4 x ^ { 3 } - 3 x + 23$ and $g ( x ) = 4 x ^ { 2 } + 2 x$

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = x ^ { 2 } - x - 9 , g ( x ) = x - 1$ Find $( f \cdot g ) ( x )$ .

Given f(x) and g(x), find the indicated composition and state its domain. - $f ( x ) = 3 x + 15 , \quad g ( x ) = 2 x - 1$ Find $( g \circ f ) ( x )$ .

Solve the problem. -What is the maximum product of two positive numbers whose sum is $32 ?$

Given f(x) and g(x), find the indicated composition and state its domain. -For $g ( x ) = \sqrt { x + 4 }$ and $h ( x ) = \frac { 1 } { x - 7 }$ , what is the domain of $h \cdot g$ ?

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = - x ^ { 2 } + 15 x - 56$

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = x ^ { 2 } + 3 x - 18 , g ( x ) = x + 6$ Find $\left( \frac { f } { g } \right) ( x )$ .

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = - 10 x , g ( x ) = - 7 x + 5$ Find $( f \cdot g ) ( x )$ .

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = x + 4 , g ( x ) = 2 x - 3$ Find $\left( \frac { f } { g } \right) ( x )$ .

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value - $f ( x ) = 5 ( x - 8 ) ^ { 2 } - 3$

Solve the problem. -A gardener is fencing off a rectangular area with a fixed perimeter of $80 \mathrm { ft }$ . What is the maximum area?

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = ( x + 6 ) ^ { 2 } + 10$

For the given functions f(x) and g(x), find (f ∙ g)(x) or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f ( x ) = ( x - 5 ) ^ { 2 }$

Without graphing the function, state the shift(s) that are applied to the graph of f(x) = x2 to graph the given function. If the graph of f(x) = x2 must be rotated about the x-axis, state this. - $f ( x ) = x ^ { 2 } + 2$

Solve the problem. -It costs $400 to start up a business of selling hot dogs. Each hot dog costs $0.55 to produce. Find the cost function C(x) = mx + b whose input is the number of hot dogs and whose output is the total Cost.

Find the x- and y-intercepts. If no x-intercepts exist, state so. - $f ( x ) = 2 x ^ { 2 } + 5 x - 3$

Solve the problem. -What is the minimum product of two numbers whose difference is 84?

Solve the problem. - $f ( x ) = \sqrt { x } - 3$