Mini Lecture
Graph.

1. \(4x+5y=20\)

2. \(y=3x-2\)

3. \(y=-\displaystyle\frac{2}{3}+1\)

The table shows the prices of used Ford Mustangs in the local paper. Figure 7 is a scatter diagram of those cars. Why is the data not a function?

Mini Lecture
Are these functions?

1. \(\{(7,-1), (3,-1), (7,4)\}\)

2. \(\{(4,1), (1,4), (-1,-4)\}\)

A balloon has the shape of a sphere with a radius of \(3\) inches. Use \(V(r)=\displaystyle\frac{4}{3}\pi r^3\) and \(S(r)=4\pi r^2\) to find the volume and the surface area.

Mini Lecture
Let \(f(x)=2x-1\) and \(g(x)=x^2-4\) find

Mini Lecture
Let \(f(x)=2x^2-8\), find:

1. \(f(0)\)

2. \(f(-3)\)

3. \(f(a)\)

4. \(f(a-3)\)

5. Graph \(f(x)=x^2\) and find \(f(1)\), \(f(2)\), and \(f(3)\).

Mini Lecture
Let \(f(x)=2x-1\) and \(g(x)=x^2-4\) find

1. Find \(x\) if \(f(x)=0\)

2. Find \(x\) if \(g(x)=0\)

3. Find \(x\) if \(f(x)=g(x)\)

The function \(N = f(p)\) graphed in Figure \(15\) gives the number of people who have given eye pressure level \(p\) from a sample of \(100\) people with healthy eyes, and the function \(g\) gives us the number of people with pressure level \(p\) in a sample of \(100\) glaucoma patients.

a. Write a formula for \(g\) as a transformation of \(f\).

b. For what pressure readings could a doctor be fairly certain that a patient has glaucoma?

Graph \(y = |x - 3| + 4\).

The function \(A = f(t)\) graphed in Figure \(18\) gives a person’s blood alcohol level \(t\) hours after drinking a martini. Sketch a graph of \(g(t) = 2f(t)\) and explain what it tells you.

Graph \(f(x) = \frac{1}{4}(x + 4)^2 + 2\).

For temperatures greater than \(10^\circ\), the average daily number of soft drinks sold, \(s\) (in hundreds), in the a city depends on the temperature, \(t\), as \[s(t) = 1, 200 + 23t + 600(t - 10)^{1/3}\]

The number, in hundreds, of soft drink aluminum cans recycled, \(r\), depends on the number of soft drinks sold, \(s\), as \(r(s) = s^{3/4}\)

a. Give some reasonable numbers for the domain of the function \(s\).

b. How many cans are sold when the temperature is \(27^\circ C\)?

c. How many cans are recycled when the temperature is \(27^\circ C\)?

d. Suppose we want to use the Fahrenheit temperature scale, instead of the Celsius scale. How would the problem change?

Mini Lecture

If \(f(x) = 3x - 5\), \(g(x) = x - 2\), and \(h(x) = 3x^2 - 11x + 10\) find:

\(1\). \((f + g)(x)\) \(2\). \(\frac{h}{g}(x)\) \(3\). \((fg)(3)\)

If \(f(x) = x^2 + 3x\) and \(g(x) = 4x - 1\), find:

\(4\). \((f \circ g)(0)\) \(5\). \((g \circ f)(0)\)

\(6\). \((f \circ g)(x)\) \(7\). \((g \circ f)(x)\)

Graph and identify the \(x\)-intercept, \(y\)-intercept, and slope: \[2x+y=6\]

Graph and identify the \(x\)-intercept, \(y\)-intercept, and slope: \[y=-2x-3\]

Graph and identify the \(x\)-intercept, \(y\)-intercept, and slope: \[y=\frac{3}{2}x+4\]

Graph and identify the \(x\)-intercept, \(y\)-intercept, and slope: \[x=-2\]

Give the equation of the line through \((-1,\,3)\) that has a slope \(m=2\).

Give the equation of the line through \((3,-2)\) and \((4,-1)\).

Line \(l\) contains the point \((5,-3)\) and has a graph parallel to the graph of \(2x-5y=10\). Find the equation for \(l\).

Line \(l\) contains the point \((-1,-2)\) and has a graph perpendicular to the graph of \(y=3x-1\). Find the equation for \(l\).

Give the equation of the vertical line through \((4,-7)\).

Graph: \[3x-4y<12\]

Graph: \[y\leq -x+2\]

State the domain and range. Indicate whether the relation is a function: \[\left\{(-2,0),(-3,0),(-2,1)\right\}\]

State the domain and range. Indicate whether the relation is a function: \[y=x^2-9\]

Let \(f(x)=x-2\), \(g(x)=3x+4\) and \(h(x)=3x^2-2x-8\). Find: \(f(3)+g(2)\)

Let \(f(x)=x-2\), \(g(x)=3x+4\) and \(h(x)=3x^2-2x-8\). Find: \(h(0)+g(0)\)

Let \(f(x)=x-2\), \(g(x)=3x+4\) and \(h(x)=3x^2-2x-8\). Find: \((f\circ g)(2)\)

Let \(f(x)=x-2\), \(g(x)=3x+4\) and \(h(x)=3x^2-2x-8\). Find: \((g\circ f)(2)\)

Quantity \(y\) varies directly with the square of \(x\). If \(y\) is \(50\) when \(x\) is \(5\), find \(y\) when \(x\) is \(3\).

Quantity \(z\) varies jointly with \(x\) and the cube of \(y\). If \(z\) is \(15\) when \(x\) is \(5\) abnd \(y\) is \(2\), find \(z\) when \(x\) is \(2\) and \(y\) is \(3\).

The maximum load \((L)\) a horizontal beam can safely hold varies jointly with the width \((w)\) and the square of the depth \((d)\) and inversely with the length\((l)\). If a 10-foot beam with width \(3\) feet and depth \(4\) feet will safely hold up \(800\) pounds, how many pounds will a 12-foot beam with width \(3\) and depth \(4\) feet hold?