Exam 1: Functions and Their Graphs

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=5|x|$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=-|x|$ A) B) C) D)

Solve the problem. -A retail store buys 120 VCRs from a distributor at a cost of $200 each plus an overhead charge of $35 per order. The retail markup is 30% on the total price paid. Find the profit on the sale of one VCR.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\frac{1}{4}|x|$

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the average rate of change for the function between the given values. - $f ( x ) = 2 x - 6 ; \text { from } 1 \text { to } 3$

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=x^{3}+1$ A) B) C) D)

Solve the problem. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is h feet, express the volume of the silo as a function of h. A) $V ( h ) = 100 \pi ( h - 10 ) + \frac { 2000 } { 3 } \pi$ B) $V ( h ) = 4100 \pi ( h - 10 ) + \frac { 500 } { 7 } \pi$ C) $V ( h ) = 100 \pi h + \frac { 4000 } { 3 } \pi h ^ { 2 }$ D) $V ( h ) = 100 \pi \left( h ^ { 2 } - 10 \right) + \frac { 5000 } { 3 } \pi$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 5 x ^ { 3 }$

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. -f(x) = 5x - 8 A) 0 B) $5 + \frac { 10 ( \mathrm { x } - 8 ) } { \mathrm { h } }$ C) 5 D) $5 + \frac { - 16 } { \mathrm {~h} }$

Graph the function. - $f ( x ) = | x |$ A) B) C) D)

Solve the problem. -A farmer has 1,600 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A? A) $A ( x ) = - x ^ { 2 } + 1,600 x ; \{ x \mid 0 < x < 1,600 \}$ B) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 1,600 \}$ C) $\mathrm { A } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 800 \}$ D) $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 800 \mathrm { x } ; \{ \mathrm { x } \mid 0 < \mathrm { x } < 800 \}$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,1 )$

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of $y = \sqrt { x }$ The graph is shifted down 3 units, reflected about the x-axis, and finally shifted left 2 units. A) $y = - \sqrt { x - 2 } + 3$ B) $y = - \sqrt { x + 2 } - 3$ C) $y = - \sqrt { x + 2 } + 3$ D) $y = \sqrt { - x - 2 } - 3$

Find the value for the function. - $\text { Find } f(4) \text { when } f(x)=x^{2}-4 x+3$

Graph the function. - $f ( x ) = x ^ { 3 }$ A) B) C) D)

Graph the function. - $f(x)=\sqrt[3]{x}$ A) B) C) D)

Solve the problem. -A rectangular box with volume 433 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the Base. Express the cost the box as a function of x. A) $C ( x ) = 3 x ^ { 2 } + \frac { 3,464 } { x }$ B) $C ( x ) = 4 x + \frac { 3,464 } { x ^ { 2 } }$ C) $C ( x ) = 3 x ^ { 2 } + \frac { 1,732 } { x }$ D) $C ( x ) = 2 x ^ { 2 } + \frac { 3,464 } { x }$

Solve. -If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit varies directly with the amount of voltage applied to the circuit. When 2 volts are applied to a circuit, 40 milliamperes Of current flow through the circuit. Find the new current if the voltage is increased to 15 volts.

Solve the problem. -The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 4 units long. Express the area A of the rectangle in terms of x.