exit level
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Exit Level. TAKS Preparation Unit Objective 2. Parent Functions. There are two parent functions on the TAKS test:. Linear. Quadratic. y = x ². y = x. Opens up. Vertex at (0, 0). y axis is axis of symmetry. 2, Ab2A. Domain and Range. Domain is the set of all x values - PowerPoint PPT PresentationTRANSCRIPT
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Exit Level
TAKS Preparation UnitObjective 2
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Parent Functions• There are two parent functions on the
TAKS test:
2, Ab2A
Linear Quadratic
y = x y = x²
y axis is axis of symmetry
Vertex at (0, 0)
Opens up
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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
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Domain and Range, cont…• Example of finding the Domain
Domain:____ < x ≤ ____
-3 2
2, Ab2B
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Domain and Range, cont…• Example of finding the Range
Range
____ ≤ y < ____
5
-4
2, Ab2B
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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
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Interpreting Graphs, cont…• The slope of lines indicates speed
– Steep line means rapid speed– Flat line means no movement
2, Ab2C
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
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Scatter Plots
Correlation
Positive Negative No
2, Ab2D
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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
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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
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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
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Patterns, cont…• Here’s an example:
Figure # of squares
1 1
2 4
3 9
4 16
Make a table
3, Ac3B
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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
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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, Ab4A
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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, Ab4A
- 4x - 4x-2y ≤ -4x + 5-2 -2 -2Because you
divided by a negative, you must flip the ≤ to !
y 2x – 2.5
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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
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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
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Simplifying Expressions• Use properties to simplify completely
• Example: Which expression is equivalent to (5t – 4)6t – (5t – 4)(t + 1)?
3, Ab4B
Multiply to eliminate parentheses
30t² - 24t – 5t² - 5t + 4t + 4
30t² - 24t - 4)+5t5t²- ( - 4t
Combine like terms
25t² -25t + 4