Exam 1: Functions and Their Graphs

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. - $f(x)=(x+7)^{2}+4$

Solve. -The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$ . A measuring device is calibrated to give $\mathrm { V } = 319.2 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 570 ^ { \circ }$ and $\mathrm { P } = 25 \mathrm { lb } / \mathrm { in } ^ { 2 }$ . What is the volume on this device when the temperature is $430 ^ { \circ }$ and the pressure is $20 \mathrm { lb } / \mathrm { in } ^ { 2 }$ ?

Solve the problem. -If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 21 kilograms accelerates at a rate of 9 meters per second per second by a force, Find the rate of acceleration of an object with a mass of 7 kilograms that is pulled by the same force.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=(-x)^{3}$ A) B) C) D)

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x + 2 } ;$ from 1 to 4

Answer the question about the given function. - $\text { Given the function } f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 } \text {, is the point } ( 2 , - 3 ) \text { on the graph of } f \text { ? }$

Solve. -While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 28.8 Newtons when the car is moving at a speed of 20 kilometers per hour and the passenger has a mass of 80 Kilograms, find the force a passenger experiences when the car is moving at 70 kilometers per hour and the Passenger has a mass of 90 kilograms.

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-4,11),(-3,4),(0,-5),(3,4),(5,20)\}$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=-x^{2}$ A) B) C) D)

Match the function with the graph that best describes the situation. -The height of an animal as a function of time. A) B) C) D)

Determine whether the equation defines y as a function of x. - $x=y^{2}$

If y varies directly as x, find a linear function which relates them. - $y = 18 \text { when } x = 21$

Determine whether the equation defines y as a function of x. - $y=\frac{1}{x}$

Find the average rate of change for the function between the given values. - $f ( x ) = \sqrt { 2 x - 1 } ;$ from 1 to 5

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \sqrt { x + 24 }$

Solve the problem. -From a 48-inch by 48-inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express The volume of the box as a function of x. A) $V ( x ) = 2 x ^ { 3 } - 144 x ^ { 2 } + 48 x$ B) $V ( x ) = 2 x ^ { 3 } - 144 x ^ { 2 }$ C) $V ( x ) = 4 x ^ { 3 } - 192 x ^ { 2 } + 2,304 x$ D) $V ( x ) = 4 x ^ { 3 } - 192 x ^ { 2 }$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=-2(x+1)^{2}-3$ A) B) C) D)

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(10).

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

The graph of a function f is given. Use the graph to answer the question. -What is the domain of f?