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. - $f(x)=3(x+1)^{2}+2$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $f ( x ) = 2 + 8 x - x 2 ; ( - 5,5 )$

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

Determine whether the equation defines y as a function of x. - $x + 7 y = 5$

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).

Find the value for the function. -Find $- f ( x )$ when $f ( x ) = | x | + 9$ .

Match the correct function to the graph. -

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = f ( x + 3 )$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{ ( - 1 , - 3 ) , ( - 2 , - 2 ) , ( - 2,0 ) , ( 2,2 ) , ( 14,4 ) \}$

Determine whether the equation defines y as a function of x. - $- 4 x + x ^ { 2 } - 58 = y$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = x ^ { 2 } - 2 x$

Use the graph to find the intervals on which it is increasing, decreasing, or constant. -

Solve. -The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 890 miles Above the earth in 17 hours at a velocity of 21,000 mph, how long would it take a satellite to complete an orbit if It is at 1,700 miles above the earth at a velocity of 25,000 mph? (Use 3960 miles as the radius of the earth.)

Find the average rate of change for the function between the given values. - $f ( x ) = 4 x 2 ; \text { from } 0 \text { to } \frac { 7 } { 4 }$

Write the word or phrase that best completes each statement or answers the question. -The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is $W ( t ) = \left\{ \begin{array} { l l } t & \text { if } 0 \leq v < 1.79 \\33 - \frac { ( 10.45 + 10 \sqrt { v } - v ) ( 33 - t ) } { 22.04 } & \text { if } 1.79 \leq v < 20 \\33 - 1.5958 ( 33 - t ) & \text { if } v \geq 20\end{array} \right.$ where v represents the wind speed (in meters per second) and t represents the air temperature (°C). Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.)

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = 8 x$

Answer the question about the given function. -Given the function $f ( x ) = 3 x ^ { 2 } - 6 x + 7$ , what is the domain of $f$ ?

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } - 7 \leq x < - 7 \\| x | & \text { if } - 7 \leq x < 7 \\\sqrt [ 3 ] { x } & \text { if } 7 \leq x \leq 26\end{array} \right.$

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.