Sure! Below is a response that follows the structure you've provided for your math practice assignment.
Function of the Day:
(You may want to write a specific function here based on what has been taught in class).
What do you know?
- I know what a function is.
- I know how to evaluate functions at given values.
- I understand the difference between linear and nonlinear functions.
- I am familiar with input and output values of a function.
- I can identify the domain and range of a function.
- I know how to graph functions on a coordinate plane.
- I understand the concept of a function's slope.
- I can explain the significance of the y-intercept in a linear function.
- I understand how to find the inverse of a function.
- I can apply functions to solve real-world problems.
Vocabulary Terms - Define/Illustrate
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Scientific Notation: A method of expressing very large or very small numbers using powers of ten. For example, 3,000 can be written as \(3 \times 10^3\).
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Our number system is based on: Base 10 (the decimal system), which uses digits 0-9.
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Coefficient: A numerical factor in a term of an algebraic expression. For example, in the term \(3x^2\), 3 is the coefficient.
5 Problems - SHOW ALL WORK!
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Round 8.266 to the nearest tenths.
To round 8.266 to the nearest tenths place, we look at the hundredths place, which is 6:
- The tenths place is 2.
- Since the digit in the hundredths place (6) is 5 or greater, we round the tenths place up from 2 to 3.
Thus, 8.266 rounded to the nearest tenths is 8.3.
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Write in standard form: The distance from Earth to Jupiter is 553.26 million miles.
To write this in standard form, we convert it into numbers:
- 553.26 million = 553.26 × 1,000,000 = 553,260,000.
So, in standard form, it is written as 5.5326 × 10^8.
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Write in standard form: A red blood cell’s diameter is about 7 millionths of a meter.
7 millionths = \(7 \times 10^{-6}\) meters.
Thus, in standard form, it is 7 × 10^-6.
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Los Angeles has a population of 3,971,883 people. Estimate the population as a single digit number times a power of 10.
The significant digits in 3,971,883 are 3.97, and it is closest to \(4\) when rounding.
- To account for the magnitude, we have 3,971,883 = \(4 \times 10^6\).
So, the estimate is approximately 4 × 10^6.
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Write 100,000 in exponential notation with a base of 10.
100,000 can be expressed as \(10^5\) because \(10^5 = 100,000\).
What do I need help with?
- I would like to review concepts of graphing functions.
- I need clarification on identifying the domain and range of different functions.
- I need more practice with converting between standard form and scientific notation.
Feel free to adjust any part of the content or add specific examples or personal comments based on what you’re learning!