Chapter 5 Unit Review

1. Representing a Relation- With an Arrow Diagram- With ordered pairs- With a table

ExampleRepresent the following relation as an Arrow Diagram and as ordered pairs.

Word Number of vowels

Santa 2Tree 2Chocolate 4Greetings 3Lights 1

2. Dependent and Independent variables- Think of “what depends on what”- Time is usually the independent variable

ExampleThe temperature, T degrees Celsius, of the Earth’s interior is a function of the distance, d kilometers, below the surface: T(d) = 10d + 20. Identify the dependent and independent variables.

3. Interpreting a graph- Understanding what the variables are and what the data represents.

Examples

4. Function Notation- Writing as an equation with 2 variables.- Special Case: y = f(x)

ExamplesWrite the following in function notation:

a) H = 7t + 2 b) y = 12x-3 c) M = 12x + 36

Write the following as an equation with 2 variables:

a) f(x) = 2x+9 b) G(x) = 24x – 3 d) H(s) = 98s – 3

For each function in part 1, find the value of the function if the independent variable = 1.

Find the value of the independent variable if f(x) = 21

a) f(x) = 10x – 9 b) f(x) = x + 30 c) f(x) = 2x + 1

If f (x) = 2x - 1, what is the value of f (-3) ?

A. –7B. – 4C. –1D. 5

5. How to determine if a relation is a function- Looking at ordered pairs or a table.- Vertical line test- Has to be one-to-one- There can’t be 2 identical x-values (or 2 of the same numbers in the domain)

ExamplesDetermine where the relation is a function. Justify your answer

a) {(1,1),(2,2),(3,3),(4,4)}{(1,4),(2,6),(5,8),(2,9)}

6. Difference between a discrete graph and a continuous graph- Discrete graph is dotted. No in between values are allowed (ex. Number of Cars in a Parking Lot – can’t have

half of a car, whole values only)- Continuous graph has connected dots. In between values have to be accounted for (ex. Speed of a car over a

period of time – the car will always have some speed in between seconds, like at 2.45 seconds)

7. Determining the Domain and Range of a Function of a discrete graph- By looking at a table of values

i) determine the independent and dependent variables firstii) Independent = domain, Dependent = range

- By looking at ordered pairsi) left side = Domain, right side = Range

- By looking at a graphi) x-values (horizontal) = Domain, y-values (vertical) = Range

*Remember: only list repeating numbers once and always use outside brackets!

Example

Write the domain and range for the following graph:

8. Determining the Domain and Range of a function with a continuous graph- By looking at a graph- Must represent all in between values -> use inequalities - If the function has an arrow, then some variables will go on forever- If both ends have an arrow, then Domain or Range = All real numbers

9. Determining the Rate of Change of a function- By looking at a table of values

i) Find the difference in both sets of dataii) Difference in Dependent Variables divided by Difference in Independent Variables

Example

Find the rate of change for the following linear relation:

Speed (m/s) Time (s)4 2.56 3.08 3.510 4.0

- By looking at a graph (Triangle)

i) Create a triangle between 2 points of dataii) Find the difference in the y-values (subtract)iii) Find the difference in the x-values (subtract)iv) Divide the y-difference by the x-difference

*Positive Rate of Change looks like:*Negative Rate of Change looks like:

Example

Find the rate of change of the following graph:

- By looking at the equationi) Always the number in front of the independent variable

Example

Determine the rate of change of the graph of y = -3x + 8

10. Determining the horizontal and vertical intercepts- Using a graph

i) Horizontal Intercept => where graph crosses x-axis (write as x = )

ii) Vertical Intercept => where graph crosses y-axis (write as y = )

Example

Find the horizontal and vertical intercepts of the following function

- Using the equation- For horizontal intercept => Substitute y=0 into equation and solve

for x.- For vertical intercept => Substitute x=0 into equation and solve for

y.

ExamplesDetermine the x-intercept of the graph of y = (x + 8)/2

A. –16B. –8C. 4D. 8

Determine the y-intercept of the graph of 9x + 6y - 72 = 0 .A. –72B. 6C. 8D. 12