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. - $f(x)=\frac{1}{5} x^{2}$

Solve the problem. -If a rock falls from a height of 80 meters on Earth, the height $\mathrm { H }$ (in meters) after $\mathrm { x }$ seconds is approximately $\mathrm { H } ( \mathrm { x } ) = 80 - 4.9 \mathrm { x } ^ { 2 }$ What is the height of the rock when $x = 1.5$ seconds? Round to the nearest hundredth, if necessary.

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. - $f(x)=|x|+1$

The graph of a piecewise-defined function is given. Write a definition for the function. -

Solve the problem. -A rectangular sign is being designed so that the length of its base, in feet, is 10 feet less than 4 times the height, h. Express the area of the sign as a function of $h$ .

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

Solve the problem. -Jacey, a commissioned salesperson, earns $140 base pay plus $35 per item sold. Express Jacey's gross salary G as a function of the number x of items sold.

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Answer the question about the given function. -Given the function $f ( x ) = \frac { x ^ { 2 } + 5 } { x - 3 }$ , list the $x$ -intercepts, if any, of the graph of $f$ .

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.

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

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. - $f(x)=|x+6|-6$

Find the value for the function. -Find $f ( - x )$ when $f ( x ) = \frac { x } { x ^ { 2 } + 1 }$

Determine whether the equation defines y as a function of x. - $y = | x |$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = \frac { 1 } { 7 x }$

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. - $f ( x ) = \frac { 1 } { x } + 2$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 1 } { x ^ { 2 } }$

Graph the function. - $f(x)=\left\{\begin{array}{ll}x-1 & \text { if } x<1 \\-5 & \text { if } x \geq 1\end{array}\right.$

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. - $f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$

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. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 ; ( - 5,5 )$