Download Exit Level

Exit Level
TAKS Preparation Unit
Objective 2
© A Very Good Teacher 2007
Parent Functions
• There are two parent functions on the
TAKS test:
Linear
Quadratic
y = x²
y=x
Opens up
Vertex at (0, 0)
y axis is axis of
symmetry
2, Ab2A
© A Very Good Teacher 2007
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, Ab2B
© A Very Good Teacher 2007
Domain and Range, cont…
• Example of finding the Domain
Domain:
____ < x ≤ ____
-3
2
2, Ab2B
© A Very Good Teacher 2007
Domain and Range, cont…
• Example of finding the Range
5
Range
____ ≤ y < ____
-4
2, Ab2B
© A Very Good Teacher 2007
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, Ab2C
© A Very Good Teacher 2007
Interpreting Graphs, cont…
• The slope of lines indicates speed
– Steep line means rapid speed
– Flat line means no movement
No movement
1000 ft in 1 min
fastest speed
1000 ft in 2 min
or 500 ft per min
500 ft in 2 min
or 250 ft per min
500 ft in 1 min
2, Ab2C
© A Very Good Teacher 2007
Scatter Plots
Correlation
Positive
Negative
2, Ab2D
No
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
Patterns, cont…
• Here’s an example: Make a table
Figure
# of
squares
1
2
3
4
1
4
9
16
3, Ac3B
© A Very Good Teacher 2007
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
© A Very Good Teacher 2007
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
y=½
9 – 2y = 8
-9
-9
– 2y = -1
-2 -2
3, Ab4A
© A Very Good Teacher 2007
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
- 4x
- 4x
-2y ≤ -4x + 5
Because you
-2
-2 -2
divided by a
negative, you
must flip the ≤
to !
y  2x – 2.5
3, Ab4A
© A Very Good Teacher 2007
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, Ab4A
© A Very Good Teacher 2007
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, Ab4A
© A Very Good Teacher 2007
Simplifying Expressions
• Use properties to simplify completely
• Example: Which expression is equivalent
to (5t – 4)6t – (5t – 4)(t + 1)?
Multiply to eliminate
30t² - 24t - (5t² +5t - 4t - 4)
parentheses
30t² - 24t – 5t² - 5t + 4t + 4
Combine like terms
25t² -25t + 4
3, Ab4B
© A Very Good Teacher 2007