Linear Functions
Define what it means for a function to be linear. Give an example or draw it out.
Answers will vary.
In a sequence, what do the three trailing dots represent at the end of the numbers? For example:
1, 2, 3, 4, ...
The trailing dots represent that the sequence will continue on forever.
A variable represents a placeholder for a number.
Is 4.5 a whole number? Why or why not?
No, it is not, because it includes an additional decimal, 0.5.
What does the radical symbol represent in mathematics?
The radical symbol represents the square root.
There is a slope-intercept equation for lines, written as y = mx + b. What do m and b represent in this equation?
True or false: the next number in the below sequence will be 18.
1, 3, 5, 7, 9, 11, 13, 15, ...
False. The next number will be 17.
Is it possible to divide by zero in mathematics? Explain why or why not.
No, it is not possible. Answers for explanations will vary.
What are the natural numbers? What can we also call them?
The natural numbers are also known as the counting numbers. They are the numbers in the set:
1, 2, 3, 4, 5, 6, 7, 8, 9...
Give a real-world example of something that has volume.
Answers will vary.
How do we find the slope of a line from two points? Provide the equation.
We find the slope, m, by doing y2 - y1 / x2 - x1.
Find the next number in the sequence:
4, 5, 8, 13, 20, ...
Solve the following equation using the chunking strategy:
3x + 8 = 29
x = 7.
Is the square root of 16 a rational number? Explain.
Yes. The square root of 16 is 4, meaning it is a whole, rational number, as it can be represented by a fraction where the numerator and denominator are integers.
Does the following equation represent a function? Why or why not?
x = 10.
No, it represents a vertical line, which does not pass the vertical line test. It also tells us that for one input, there are infinitely many outputs.
I have a linear function with points (0, 10) and (2, 20). Find the slope of the line.
The slope of this line will be m = (20-10)/(2-0) = 5.
Answers will vary.
Solve the following equation using the chunking method:
5y + 2y - 5 = 30
y = 5.
Do the integers include negative numbers?
Yes. Integers include negative numbers.
Recall your mathematics project, and give a brief summary of what you learned.
Answers will vary.
I have two linear equations:
y = 15x + 75 and
y = -10x + 80
Which function has the greater rate of change? Explain.
y = 15x + 75 has the greater rate of change because 15 is greater than 10.
Find the next number in the sequence:
3, 6, 18, 72, ...
The next number will be 360.
I give a system of equations in class to solve.
Kaloni gets a final answer of 2 = 2.
Merje gets a final answer of x = 18.
Esteban gets a final answer of 10 = 17.
What does each answer mean, and how many solutions do they represent? What does this look like on a graph?
Kaloni's answer represents infinitely many solutions, meaning they are the same line. Merje's represents one solution, meaning the two lines intersect once. Esteban's represents no solutions, meaning the lines are parallel.
Give an example of an irrational number.
Pi is irrational.
Does the following scenario represent a function? Explain why or why not.
Ms. Cleo sends Ms. Blair a letter in the mail, and Ms. Blair opens and reads it.
Yes, as the input (the letter Ms. Cleo wrote) is received by ONE output (Ms. Blair).