Homework 1 Assignment

1. Read through Lessons 1.2 and 1.3 using the study guide below.
2. Answer the study guide questions in blue below. Email your answers to me.
3. Watch the section videos as needed.
4. Complete the homework assignment on course compass.

Section 1.2 Objectives and Study Guide

1. Determine whether a correspondence is a relation or a function.
   • A function is a relationship between two sets of numbers where each member of the first set has only one corresponding value in the second set. You can think of a function as a machine with inputs and outputs. You put a value from the first set (called the domain) into the function; the function ouputs a specific number, a number always associated with that input; this number is a member of the second set (called the range).
   • Examples of functions:
     • The function defined by the following ordered pairs (the first number is the input, the second number is the output): (1, 2), (2, 3), (3, 2). Notice that you can have more than one input yielding the output “2″.
     • The function defined by the following relationship: The outdoor temperature as a function of time. You would write this T(t), where T = Temperature and t = time. Here the domain, or inputs, are a set of time values. The range, or outputs, are a set of temperature values. So, each time input is assigned a specific temperature value. You cannot have one time yielding two different temperatures, so this is indeed a function.
     • The function f(x) = 2x + 3 or g(x) = x^2. Each input has a unique output.
   • A relation is a relationship between two sets of numbers where each member of the first set has at least one corresponding value in the second set. So the requirements for a relation are not as strict as they are for a function.
   • Question 1: Describe a real-world function relationship as I did above. Include a description of the domain and range.
2. Find function values, or outputs, using a function or graph.
   • The output is the function value, or y-value, associated with the input, or x-value.
3. Graph functions.
   • Plot ordered pairs (x, y) and sketch the graph connecting the points.
4. Determine whether a graph is or is not a function.
   • If a relationship is a function, then the input will have no more than one output. Graphically, this means that an x-value will have only one associated y-value, or that a vertical line can only pass through a function in one place. If it were to pass through the function in two places, then there would be two y-values for the given x-value, and the relation would not be a function.
   • Question 2: Does the graph below represent a function? Explain your answer.
5. Find the domain and range of a function.
   • Remember, the domain is all possible inputs and the range is all possible outputs. So for a function like f(x) = 1/x, the domain would be everything except for zero. Zero is not in the domain because division by zero is undefined. We can express this in two ways:
     • In Set-Builder Notation: D = {x| x ≠ 0}. You read this “The Domain is equal to the set of all x-values such that x is not equal to zero.” The brackets { } denote a set. The line | means “such that”.
     • In Interval Notation: D: (-∞, 0), (0, ∞). This says “the domain includes negative infinity to zero and zero to infinity, but excludes zero.” The parentheses ( ) denote that the endpoint is NOT included. If you need to include the endpoint use the square brackets [ ].
   • Question 3: Write the domain of the function f(x) = 1/(x-2)
     • In set-builder notation.
     • In interval notation.
6. Solve Applied Problems using Functions.

Section 1.3 Objectives and Study Guide

1. Determine the slope of a line, given two points on the line.
   • Slope is found by the change in y, divided by the change in x. You can also think of this as “rise” over “run” or (y2 – y1)/(x2 – x1).
   • For horizontal lines (y = constant), the slope is always zero, because the change in y is zero.
   • For vertical lines (x = constant), the slope is always undefined, because the change in x is zero and division by zero is undefined.
2. Solve applied problems involving slope and linear functions.