Graph each function. Give the domain and range. $f(x)=2^{x-1}+2$

The area of a trapezoid is the product of one half the height and the sum of both bases. If h is the height,

$$b_1$$

is one base, and

$$b_2$$

is the second base, write an expression for the area of the trapezoid.

A sled initially at rest has a mass of $52.0 \mathrm{~kg}$, including all of its contents. A block with a mass of $13.5 \mathrm{~kg}$ is ejected to the left at a speed of $13.6 \mathrm{~m} / \mathrm{s}$. What is the speed of the sled and the remaining contents?

Sketch a graph to illustrate that a system of three linear equations with two variables can have exactly one solution.

Graph the linear system. Then use the graph to tell whether the linear system has one solution, no solution, or infinitely many solutions.

$$\left. \begin{array} { l } { 3 x - y = - 9 } \\ { 3 x + 5 y = - 15 } \end{array} \right.$$

Find the domain and range of the relation. Is the relation a function?

$$\{(a, b),(a, c),(d, e)\}$$

Find the domain and range of the function. $f(x, y)=\sqrt{9-6 x^{2}+y^{2}}$

Use a graphing calculator to graph the equation corresponding to the inequality. From the display of the graphing calculator, locate one ordered pair in the solution set to the system and check that it satisfies all inequalities of the system. Answers may vary.

$$\begin{aligned} &y>2^{x+2} \\ &y<x^3-3 x \end{aligned}$$

Informal observation, focus groups, and qualitative surveys in behavioral research are examples of ______________.

Determine whether each system of linear equations has (a) one and only one solution, (b) infinitely many solutions, or (c) no solution. Find all solutions whenever they exist.

$$\begin{aligned} 2 x-4 y & =-10 \\ 3 x+2 y & = 1 \end{aligned}$$

Use the given function f to: Find the domain and the range of $f ^{-1}$. $f(x) = ln(x + 4)$

A wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions $150 \mathrm{~mm} \times 250 \mathrm{~mm}$, and the channel has a uniform thickness of $6.5 \mathrm{~mm}$. If the allowable stresses in the wood and aluminum are 8 $\mathrm{MPa}$ and $38\ \mathrm{MPa}$, respectively, and if their moduli of elasticity are in the ratio $1$ to $6$ , what is the maximum allowable bending moment for the beam?

Graph the function. Write the domain and range as inequalities.

$f(x)=3-\sqrt{x}$

Graph the system and determine the number of solutions that it has. If it has one solution, name it. 2x + 3y = 4, 2x + 3y = -1