© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 2

© A Very Good Teacher 2007

Exit Level

TAKS Preparation UnitObjective 2


Parent Functions• There are two parent functions on the

TAKS test:

2, A.02A

Linear Quadratic

y = x y = x²

y axis is axis of symmetry

Vertex at (0, 0)

Opens up


Domain and Range• Domain is the set of all x values• Range is the set of all y values

• To find domain: examine the right and left boundaries of the function

• To find range: examine the top and bottom boundaries of the function

• Whenever a function has two boundaries, both signs should be less than (< or ≤).

2, A.02B


Domain and Range, cont…• Example of finding the Domain

Domain:____ < x ≤ ____

-3 2

2, A.02B


Domain and Range, cont…• Example of finding the Range

Range

____ ≤ y < ____

5

-4

2, A.02B


Interpreting Graphs

• Pay attention to labels on x and y axes

• A straight line indicates constant rate of change (slope)

• A curved line indicates a changing rate

• More than one straight lines indicates rapidly changing constant rates

2, A.02C


Interpreting Graphs, cont…• The slope of lines indicates speed

– Steep line means rapid speed– Flat line means no movement

2, A.02C

No movement

1000 ft in 1 min fastest speed

500 ft in 1 min

1000 ft in 2 min or 500 ft per min

500 ft in 2 min or 250 ft per min


Scatter Plots

Correlation

Positive Negative No

2, A.02D


Using symbols• Focus on the meaning of words in a

mathematical context

• For Example:More, more than, in addition, …. Mean … +

Less, less than, difference …. Mean … -

Times, per, each, … Mean … x

Per, each, dividend … Mean … ÷

Is or other verbs … Mean … =

The goal is to turn a sentence into an equation.

3, Ac3A


Using symbols, cont…Here is a simple example:

The area of a circle is equivalent to pi times the radius squared.

A = π • r ²

So, you would look for the answer A = πr²

3, Ac3A


Patterns• Given a geometric sequence,

you must determine the equation for the function.

1. Make a table to represent the sequence

2. Use STAT to calculate the answer

3. Find the answer that fits the calculator answer

3, Ac3B


Patterns, cont…• Here’s an example:

Figure # of squares

1 1

2 4

3 9

4 16

Make a table

3, Ac3B


Patterns, cont…• Now use STAT to calculate the equation.

STAT ENTER NUMBERS STAT

5, ENTER

Look for an answer that has an equation like y = x².

3, Ac3B


Solving Equations and Inequalities

• Substitute given values

• Use inverse operations to solve

• Example: If (2.25, y) is a solution to the equation 4x – 2y = 8, what is the value of y?

4x – 2y = 8

4(2.25) – 2y = 8

9 – 2y = 8-9 -9

– 2y = -1-2 -2

y = ½

3, A.04A


Solving Equations and Inequalities, cont…• Convert inequalities from Standard form (Ax +

By > C) to y = mx + b form.• Use the same steps as you would for an equation, but

remember that if you multiply or divide by a negative number, you must flip the inequality sign!

• Example: 4x – 2y ≤ 5

3, A.04A

- 4x - 4x-2y ≤ -4x + 5-2 -2 -2Because you

divided by a negative, you must flip the ≤ to !

y 2x – 2.5


Solving Equations and Inequalities, cont…

• Given a function like y = 3x² + 2x – 4 and a set of independent variables like {-1, 0, 1, 2} and asked to find a corresponding dependent variable

• Remember that independent variables represent the x values and dependent variables represent y values

• Just use the calculator to graph the function and look at the table to identify the corresponding y values

3, A.04A


Solving Equations and Inequalities, cont…

• Example: A function is described by the equation y = 3x² + 2x – 4, in which y is dependent on x. If a value for the independent variable is selected from the set {-1, 0, 1, 2}, which of the following is a corresponding dependent value?

The answer must be from the y values that correspond to the x values listed in the question. So, the answer must be one of {-3, -4, 1, 12}.

3, A.04A


Simplifying Expressions• Use properties to simplify completely

• Example: Which expression is equivalent to (5t – 4)6t – (5t – 4)(t + 1)?

3, A.04B

Multiply to eliminate parentheses

30t² - 24t – 5t² - 5t + 4t + 4

30t² - 24t - 4)+5t5t²- ( - 4t

Combine like terms

25t² -25t + 4

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© A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 2