1. TAKS Preparation Unit Objective 1
Grade 9
Student Version
TAKS Preparation Unit
Objective 1

2. Independent and Dependent Quantities
Independent and Dependent Quantities must be variables (_______), not constants (_________).
Independent Quantities are often quantities that cannot be controlled
Dependent Quantities change as a result of the Independent Quantities
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3. Independent and Dependent Quantities, continued…
In an equation, x represents the __________ quantity and y represents the _________ quantity
Ex: y = 2x + 3
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4. Independent and Dependent Quantities, continued…
Sometimes equations have other variables, not x and y.
Ex. d = 54t
The variable by itself is always _________!
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5. Functions and their equations, continued…
To find the equation of a function when you are given the table, use the feature of your graphing calculator.
Enter the table into the calculator using L1 for x and L2 for y.
Then return to and arrow over to CALC and choose the appropriate function type.
Press Enter to view equation.
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6. Functions and their equations, continued…
How do I know what type of function to use?
All TAKS questions will either be Linear (LinReg, ax+b) or Quadratic (QuadReg)
If you aren’t sure, look at the answers and see if they are linear (y = x) or quadratic (y = x²).
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7. Functions and their equations, continued…
Here’s one to try:
The table below shows the relationship between x and y. Which function best represents the relationship between the quantities in the table? x y -1 -4 1 2 8
y = 2x² - 4
y = 3x² - 4
y = 2x² + 4
y = 3x² + 4
B. y = 3x² - 4
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8. Writing and Interpreting Equations
These problems are always LINEAR equations or inequalities.
You will need to identify the slope (amount of change) and the y intercept (starting point)
Pay careful attention to math cue words
each means ______
increased means _____
decreased means _______
difference means _______
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9. Writing and Interpreting Equations, continued…
Example: The initial amount invested in a stock was $ Each year the stock increases in value by $545. Which equation represents t, the total value of the investment after y years?
t = 2000y + 545
t = 2000y – 545
t = 545y
t = 545y
C. t = 545y
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10. Multiple Representations of Functions
A function can be represented by an:
Equation
Mapping
Graph
Table
Data Points
Verbal Description
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11. Multiple Representations of Functions, cont…
Example: The function f(x) = {(1, 3), (2, 6), (3, 9), (4, 12)} can be represented several ways. Which is NOT a correct representation of the function f(x)? 1 2 3 4 6 9 12 x y A. B.
C. x is a natural number less than 5 and y is 3 times x
D. y = 3x and the domain is {1, 2, 3, 4}
A. y = .5x² + 3
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12. Creating a Table To create a table from a situation Write an equation
Put your equation in y=
Find a table that matches
A. Quadratic parent function
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13. Creating a Table, cont…
Example: Carmen receives a $50 gift card to the local movie theater. Each movie she watches costs $ Which table best describes b, the balance on her gift card after she watches m movies? A m b 1
6.75 5
33.75 7
47.25 B m b 50 1
56.75 5
83.75 7
97.25 m b 1
43.25 2
36.50 4
29.75 7 23 m b 50 1
43.25 5
16.25 7
2.75 C D
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14. Graphs of Inequalities
When given the graph of a linear inequality and asked to find the equation…
Use your calculator to graph each inequality (ignoring the inequality sign)
Then narrow down your choices and pay attention to details
A dotted line
A solid line
Shaded above
Shaded below
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15. Graphs of Inequalities, continued…
Example:
y < -2x +1.5
y < -2x + 3
y ≤ -2x + 3
y < 2x + 3
B. y < -2x + 3
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16. Interpreting Equations
When you are given a function and asked make a conclusion…
Use your calculator!
Example: Which is always correct about the quantities in the function y = x – 3?
The variable y is always 3 more than x
The variable x is always greater than the variable y
When the value of x is negative, the value of y is positive
As the value of x increases, the value of y decreases
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17. 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
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18. Interpreting Graphs, cont…
The slope of lines indicates speed
Steep line means rapid speed
Flat line means no movement
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19. Essential Vocabulary Independent Dependent Variable Equation Table
Inequality
Mapping
Graph