Math 95, Mod 1, Section 3.1 Graphing Equations Sec. 3.1, Pg 1

Math 95, Mod 1, Section 3.1 Graphing Equations Sec. 3.1, pg 1

I. Review the Rectangular Coordinate System ______

A. On the grid below locate and label the following:

Origin

x-axis: ______

y-axis: ______

Quadrants I, II, III and IV

B. On the grid below, plot the following points and name the quadrant in which the point lies:

Notice that these points are called ______

because the order in which they are written tells you which number is associated

with which axis. In the first point (3,-2), 3 is called the ______

And -2 is called the ______.

Point Quad

(3,-2)

(-4,1)

(-1,0)

(-2 ½ ,-3)

(3.5,4.5) Sec. 3.1, pg2 II. Review of M65 functions:

A: Linear: make a table of values. Use at least _____ points. These points are called ______to the equation. Or, you can use the short hand method of graphing the y-intercept of ______and the slope of ______.

Slope- intercept form:

Standard Form:

Intercepts:

When graphing non-linear equations more points will be needed to create the graph. B: Quadradic: y= x2 +2 x - 3 Each square represents 2 units.

The vertex:______y

The Axis of Symmetry (AOS):______

The x-intercept(s): ______   

The y-intercept: ______



C. Square root: y= x -1

D: Exponential: III. Two more non-linear functions: Sec. 3.1, pg 3

A. Fill out the table and graph the following Absolute Value Equation:

Ex. 1: The absolute value of a number is the distance of that number from zero. Since distance is always measured in positive units, the absolute value of any number will always be positive. The notation is: y= x

B. Step functions: These are not continuous. They are used to visualize growth or decline in step increments instead of continuous increments.

Ex. 2: Graph the cost of mailing a first class item at the US Post Office for the weights of 0 ounces to 4 ounces. M95 Sec. 3.2: Functions and Function notation: Sec. 3.2, pg 1 I. Terms:

A. Relation:

B. Domain:

C. Range:

D. Function:

II. Representations:

A. Numerical.

For each of the following, state the domain, range and whether it is a function: Ex. 1: {(0,2) ,( 1,4) ,( 1,2) ,( 2,3) ,( 3,- 2)}

Domain:______Range:______Function: ______

Ex. 2: Input, x 0 1 2 3 4 5 Output, y -2 4 -1 -2 3 2

Ex. 3:

Domain:______Range:______Function: ______B. Graphs: Sec. 3.2 pg 2 Use the vertical line test (VLT) for the following:

Ex. 4: 4x2+ 9 y 2 = 36 Each square represents 1 unit.

Domain:______

Range:______Function: ______

Ex. 5: h( x )= x - 4 Each square represents 1 unit.

Domain:______

Range:______

Function: ______

C. Equations: Sketch a graph and use the VLT

2 Ex. 6: y=( x - 3)

D. Verbal Description:

Ex. 7: In 2008, LBCC paid $0.48 per mile when a faculty member used his/her own vehicle for transportation to a sanctioned event. Write a symbolic description for the cost (C) of driving m miles. State the domain and range. Find C(130) and interpret what it means. Sec. 3.2 pg 3

III. Review function notation: f(x) is read “f of x”. It represents the function f written in terms of x.

y = f(x) so x is the ______

and f(x) is the ______

Ex. 8: Use the graph from Ex. 5 h( x )= x - 4 Each sq. represents 1 unit. to find: h(-2)=______What point does this represent on the graph?______h(-3) = ______What point does this represent on the graph?______h(5) = ______What point does this represent on the graph?______h(0) = ______What point does this represent on the graph?______

骣 2 Ex. 9: Given the function: f( x )= - 3 x + 5 find f 琪 - 桫 3

Ex. 10: Given the function: g( x )= - x2 - 3 find g ( - 2) and g ( a ) and g ( a + 2)

Ex. 11: P( t )= 1.08(1.0139)t represents the population in billions in India where t is the number of years after 2005. Find P(0) and P(12) and describe what they represent. Math 95, Mod 1, Sec. 3.3 Graphing Linear functions M95, Sec. 3.3, pg 1 I. Reviewing Linear Functions:

Ex. 1: Which of the following graphs represent linear functions (caution!)? Each square represents 1 unit. a) b) c) d)

y y y y    

   

   

    x x x x                                                

II. Graphing

Ex. 2: Write equations for the straight lines in Ex. 1 a) b) c) d)

Ex. 3: Graph the following linear equations:

III. Verbal Descriptions: Sec. 3.3, pg 2

Determine whether the following verbal description is of a linear function. If it is, write an equation to represent it. Remember that linear functions must increase or decrease at a constant rate. Graph the equation and answer the questions.

Ex. 4: The Maytag repairman comes to my house to repair my washing machine. He charges me $40 per hour for the work he does and an additional $35 for the "house call".

a) What is the domain of this relation?

b) Is this relation a function? Why or why not?

c) From your graph, find the cost of a 2.5 hour repair.

d) Use your equation to find out how long it took to repair the machine if the total bill was $205. Compare your results to the graph.

e) What does the point (0,35) represent in this situation?