Exam 4: Additional Topics With Functions

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = x ^ { 2 } , g ( x ) = ( x - 6 ) ^ { 2 } - 5$

Fill in each blank with the appropriate response. -The graph of $y = - 6 ( x - 2 ) ^ { 2 } + 8$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontallyــــــــــ units to theـــــــــــ , vertically stretching by a factor ofــــــــــ , reflecting across the ــــــــــــ-axis, and shifting vertically ـــــــــunits in the ــــــــdirection.

Determine whether or not the function is one-to-one. - $f ( x ) = x ^ { 2 } - 4$

Use the quadratic formula or graphing methods to - $8 x ^ { 2 } < 8 x + 8$

Assume that the elevation E , in feet, of a sag in a proposed route is given by $E ( x ) = 0.000039 x ^ { 2 } - 0.25 x + 1300$ where x represents the horizontal distance in feet along the proposed route and $0 \leq x \leq 5000$ . For what x-values is the elevation 1100 feet or more? Round your answer to the nearest foot.

A rectangular enclosure must have an area of at least 2400yd² . If 220yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt [ 3 ] { 3 x - 7 } , g ( x ) = \frac { x ^ { 3 } + 7 } { 3 }$

Find the specified domain and express it in interval notation. -For $f ( x ) = \sqrt { x - 3 }$ and $g ( x ) = x - 7$ , what is the domain of $g / f$ ?

Solve $f ( x ) \geq g ( x$

If a rocket is propelled upward from ground level, its height h in meters after t sec is given by h(t)= $- 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$ During what interval of time will the rocket be higher than 205.8 m ?

Determine whether the function is even, odd, or neither. - $f ( x ) = x ^ { 3 } - \frac { 1 } { x }$

A retail store buys 175 VCRs from a distributor at a cost of $235 each plus an overhead charge of $45 per order. The retail markup is 40% on the total price paid. Find the profit on the sale of one VCR.

On May 13, 2006, each Euro was worth 1.43921 Canadian dollars and each Japanese Yen was worth 0.00703195 Euros. Find the value of 1000 Japanese Yen in Canadian dollars on May 13th, 2006. Round your answer to two Decimal places.

Solve the equation - $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

A size 8 dress in Country C is size 48 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x)=2( x +16) . Find a formula for the inverse of this function.

Determine whether the function is one-to-one. -The function that pairs students' ID numbers with their GPAs.

A manufacturer's cost is given by $C = 500 \sqrt [ 3 ] { n } + 512$ , where $C$ is the cost and $n$ is the number of parts produced. Describe the transformations needed to obtain the graph of this function from the graph of $y = \sqrt { n }$ .

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x } + 3$

Solve the equation - $\sqrt { p ^ { 2 } - 3 p + 64 } = p + 5$

Determine whether the function is even, odd, or neither. - $y = \frac { 5 } { x }$