Exam 1: Functions and Their Graphs

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 3 x ^ { 2 } + 9 x - 3 ; ( - 5,5 )$

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 17 minutes requires 10.2 gallons of water. Find the amount of water used in a shower Lasting 12 minutes.

Match the graph to the function listed whose graph most resembles the one given. -

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. - $f ( x ) = 8 x ^ { 3 } + 7 x ^ { 2 } + 8 ; \text { from } - 9 \text { to } 1$

Solve the problem. -The volume V of a square-based pyramid with base sides s and height h is $V = \frac { 1 } { 3 } s ^ { 2 } h$ If the height is half of the length of a base side, express the volume V as a function of s.

Solve the problem. -If $f ( x ) = \frac { x - B } { x - A } , f ( 4 ) = 0$ , and $f ( 9 )$ is undefined, what are the values of $A$ and $B$ ?

Solve the problem. -A rectangle that is x feet wide is inscribed in a circle of radius 36 feet. Express the area of the rectangle as a function of x. A) $A ( x ) = x ^ { 2 } \sqrt { 2,592 - x ^ { 2 } }$ B) $A ( x ) = x \sqrt { 5,184 - x ^ { 2 } }$ C) $A ( x ) = x \left( 5,184 - x ^ { 2 } \right)$ D) $A ( x ) = x \sqrt { 3,888 - x }$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $f ( x ) + 6$

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. - A) function domain: \{x\midx>0\} range: all real numbers intercept: (1,0) symmetry: none B) function domain: all real number: range: \{\mid>0\} intercept: (1,0) symmetry: none C) function domain: \{x\midx>0\} range: all real number intercept: (0,1) symmetry: origin D) $\text { not a function }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(-2,0)$

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

Graph the function. - $f ( x ) = \frac { 1 } { x }$ A) B) C) D)

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. - $f ( x ) = 0.15 x ^ { 4 } + 0.3 x ^ { 3 } - 0.8 x ^ { 2 } + 5 ; ( - 4,2 )$

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. - $f(x)=\sqrt{x+4}$ A) B) C) D)

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

Solve the problem. -A right triangle has one vertex on the graph of $y = x ^ { 2 }$ at (x, y), another at the origin, and the third on the (positive) y-axis at (0, y). Express the area A of the triangle as a function of x.

Determine whether the equation defines y as a function of x. - $x^{2}=8-x^{2}$

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 14 }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 3 - 3 x ; g ( x ) = - 5 x + 3$ Find $f + g$