Find the slope of the line passing through the points \((-1,2)\) and \((-3,4)\). Plot the points and indicate the slope on your plot.

Find the equation of the line passing through \((2,6)\) and \((-1,-2)\) in point-slope form.

Write the equation of a line with a slope of \(-4\) and \(y\)-intercept of \((0,\sqrt{2})\) in slope-intercept form. Does \((0,1)\) lie on this line? Find the \(x\)-intercept of this line.

Find the equation, in slope-intercept form, of the line whose graph is given in Figure 7.

Find the equations of the lines described below.

1. A horizontal line passing through the point \((2,3)\).

2. A vertical line passing through the point \((1,-2)\)

Write the equation \(3x+2y-4=0\) in slope-intercept form and graph the line.

Find the equation of the line parallel to \(2x-y=1\) and passing though \((2,-3)\). Write the equation in slope-intercept form.

Find an equation of the line perpendicular to \(2x+3y-1=0\) and passing through \((4,-1)\). Write the equation in slope-intercept form.

A 2012 Honda Civics value over time can be approximated by the equation \(v=-2200t+22000\) where \(t\) denotes the number of years after its purchase. Answer the following questions:

1. What will be the value of the car \(6\) years after purchase.

2. What are the slope and \(v\)-intercept, and what do they represent?

3. For what value of \(t\) will the value of the car be zero?

In 2010, there were \(1\text{,}400\) Canada Geese in a wildfire refuge. In 2016, their population increased to \(1\text{,}820\).

1. Write an equation for the population of Canada Geese, \(y\), in terms of \(x\), the number of years since 2010.

2. What are the slope and \(y\)-intercept and what do they represent?

3. When will the goose population reach \(1\text{,}960\)?

1. Find the distance between the points \((3,-5)\) and \((6,1)\).

2. Find the midpoint of the line segment joining the points \((3,-5)\) and \((6,1)\).

Write the standard form of the equation of the circle with a center at \((3,-2)\) and radius \(5\). Sketch the circle.

Write the standard form of the equation of the circle with center at \((-1,2)\) and containing the point \((1,5)\). Sketch the circle.

sketch the graph of the equation \(y-x^2=-3\)

Let \(f(x)=x^2-1\). Evaluate the following.

1. \(f(-2)\)

2. \(f\left(\dfrac{1}{2}\right)\)

3. \(f(x+1)\)

4. \(f\left(\sqrt{5}\right)\)

5. \(f(x^3)\)

Define \(H(x)\) as follows: \[H(x)= \begin{cases} 1 & \text{if } x < 0; \\ -x+1 & \text{if } 0 < x \leq 2; \\ -3 & \text{if } x > 2. \end{cases}\] Evaluate the following, if defined:

1. \(H(2)\)

2. \(H(-6)\)

3. \(H(0)\)

Find the domain of each of the following functions. Write your answer using interval notation.

1. \(g(t)=t^2+4\)

2. \(f(x)=\sqrt{4-x}\)

3. \(h(s)=\dfrac{1}{s-1}\)

4. \(h(t)=\dfrac{1}{\sqrt{4-t}}\)

Does the following set of points define s function?
\(S=\{(-1,-1), (0,0), (1,2), (2,4)\}\)

Graph the function \(g(t)=-2t^2\). Use the graph to find the domain and range of \(g\).

Graph each of the following functions. Use the graph to find the domain and range of \(f\).

1. \(f(x)=\sqrt{4-x}\)

2. \(f(x)=\lvert x\rvert\)

Graph the function \(H(x)\), defined as follows: \[H(x)= \begin{cases} x^2 & \text{if } x < 0; \\ x+1 & \text{if } 0 \leq x < 3; \\ -1 & \text{if } x \geq 2. \end{cases}\]

Use the vertical line test to determine which of the graphs in Figure 15 are graphs of functions.

The price of a product is inversely proportional to its demand. That is, \(P=\dfrac{k}{p}\), where \(P\) is the price per unit and \(q\) is the number of products demanded. If \(3000\) units are demanded at \(\$10\) per unit, how many units are demanded at \(\$6\) per unit?

Using the definitions of odd and even functions, classify the following functions as odd, even, or neither.

1. \(f(x)=\lvert x\rvert +2\)

2. \(g(x)=(x-4)^2\)

3. \(h(x)=-x^3+3x\)

For the function \(f\) given in Figure 10, find the interval(s) on which

1. \(f\) is increasing

2. \(f\) is decreasing

3. \(f\) is constant

Find the average rate of change of \(f(x)=2x^2+1\) on the following intervals:

1. \([-3,-2]\)

2. \([0,2]\)

Let \(f\) and \(g\) be two functions defined as follows:
\(f(x)=\dfrac{2}{x-4}\) and \(g(x)=3x-1\)
Find the following and determine the domain of each.

1. \((f+g)(x)\)

2. \((f-g)(x)\)

3. \((fg)(x)\)

4. \(\left(\dfrac{f}{g}\right)(x)\)

Let \(f\) and \(g\) be two functions defined as follows:
\(f(x)=2x^2-x\) and \(g(x)=\sqrt{x+1}\)
Find the following and determine the domain of each.

1. \((f+g)(-1)\)

2. \(\left(\dfrac{f}{g}\right)(3)\)

3. \((fg)(3)\)

The GlobalEx Corporation has revenues modeled by the function \(R(t)=40+2t\), where \(t\) is the number of years since 2010 and \(R(t)\) is in millions of dollars. Its operating costs are modeled by the function \(C(t)=35+1.6t\), where \(t\) is the number of years since 2010 and \(C(t)\) is in millions of dollars. Find the profit function \(P(t)\) for GlobalEx Corporation.

Let \(f(s)=s^2+1\) and \(g(s)=-2s\).

1. Find an expression for \((f\circ g)(s)\) and give the domain of \(f\circ g\).

2. Find an expression for \((g\circ f)(s)\) and give the domain of \(g\circ f\).

3. Evaluate \((f\circ g)(-1)\).

4. Evaluate \((g\circ f)(-1)\)

Let \(f(x)=\dfrac{1}{x}\) and \(g(x)=x^2-1\).

1. Find \(f\circ g\) and its domain.

2. Find \(g\circ f\) and its domain.

Make a table of values of the functions \(f(x)=\lvert x \rvert\) and \(g(x)=\lvert x \rvert -2\), for \(x=-3\), \(-2\), \(-1\), \(0\), \(1\), \(2\), \(3\). Use your table to sketch the graphs of the two functions. What are the domain and range of \(f\) and \(g\)?

Use vertical and/or horizontal shifts, along with a table of values, to graph the following functions:

1. \(g(x)=\sqrt{x+2}\)

2. \(g(x)=\lvert x+3 \rvert -2\)

The graph of \(f(x)\) is shown in Figure 20. Use it to sketch the graphs of

1. \(f(3x)\)

2. \(f(-x)+1\)