Chapter 2, Section 1 Algebra II (Honors) St. Augustine Preparatory Academy August 18, 2014

Yesterday’s Homework Page 46: 16, 18, 22, 23, 24, 34, 36, 38, 41, 43, 46 Answers: 16) -18 and 10 18) -7 and 15 22) -4, 8 23) -1, 3/2 24) 1 34) all real numbers (since the solutions overlap) 36) z 4 38) |k-50.5|≤ ) |m-1250|≤50 43) no solution (neither answer will satisfy the original equation) 46) -1/3

Going from inequality to absolute value Two steps: 1)Find the average (middle) of the two outside numbers. This is going to go into the absolute value and be subtracted from the variable 2) Subtract the two numbers on the outside of the inequality and divide by 2. Set the inequality to < the number you just found. Example: 1200 < x < )Average of = 1250 so |x-1250| 2)1300 – 1200 = 100/2 = 50 so |x-1250|<50

Our assignment questions 38) 50 ≤ k ≤ 51 Step 1: |k – 50.5| (since the ave. of 51 and 50 is 50.5) Step 2: |k-50.5|≤ 0.5 (since (51-50)/2 = 0.5) 40) 1200 ≤ m ≤ 1300 |m – 1250| (since the ave of 1200 and 1300 is 1250) |m – 1250| ≤ 50 (since ( )/2 = 50)

Chapter 2-1: Relations and Functions A relation is a set of pairs of input and output values. These can be give in the following ways:

Domain and Range Relations have both a domain and range. The domain is a set of inputs, also known as the x-coordinates. The range is the set of outputs, also known as the y-coordinates Example: With the following relation, what is the domain and range? Relation {(0,10000), (4,9744), (12,7696), (16,5904) Domain: {0, 4, 12, 16} Range: {10000, 9744, 7696, 5904}

Functions A function is a relation in which each element of the domain corresponds with exactly one element of the range Depending on the way you are given the relation, there are a couple methods you can use to tell if it is a function of not. 1) Visual inspection 2) Vertical Line Test (VLT)

Visual Inspection Are the following relations also functions? If an x-coordinate is used more than once, it is not a function. A y-coordinate can be used more than once though!

Vertical Line Test (VLT) If you can draw a vertical line (up and down) that passes through more than one point of the relation, the relation is not a function

Using the VLT

Function Rule/Notation A function rule is an equation that represents an output value in terms of an input value. Function rules can be wrote in function notation: f(x) = 3x+2 “f of x is equal to three x plus two” f(x) = x/6 “f of x is equal to x divided by six” f(x)= is essentially the same thing as y=, but it is much neater and easier to use as you start dealing with multiple equations

Using function notation Instead of being given “y=2x+3, solve for y when x = 3” we can now say: Question:f(x)=2x+3 solve if x=3 or f(3) Solution: f(3) = 2x+3 f(3) = 2(3) + 3 f(3) = f(3) = 9

Practice Page 64: 1 – 4 Page 65 : 10-12, 14-16, 17, 20, 25