Exam 4: Functions Functions and Function Notation

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 57$ when $t = 7$ and $A = \$ 27$ when $t = 1$ .

Determine whether the function is one-to-one. $y = \frac { 2 } { 5 } x$

A taxicab company charges $\$ 5$ for a trip up to 1 mile, and $\$ 4$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function.

Find the inverse of the one-to-one function. $y = 3 x + 4$

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly. $\sqrt [ 4 ] { x }$

A 330-room hotel is two-thirds filled when the nightly room rate is $100.Experience has shown that each $15 increase in cost results in 30 fewer occupied rooms.Find the nightly rate that will maximize Income.

Find the range of the function $f ( x ) = \frac { 2 x } { x - 8 }$ by finding the domain of $f ^ { - 1 } ( x )$ .

Graph the quadratic function. $f ( x ) = - 3 x ^ { 2 } + 2$

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 2 ) ^ { 2 } + 3$

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function. $( f \cdot g ) ( x )$

Graph the function. $f ( x ) = \frac { x ^ { 2 } - 3 x - 2 } { x ^ { 2 } - 4 x + 4 }$

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 4$

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 10 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 10 }$

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 10 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 10 }$