Graph Investigation Questions

What is the general shape of the graph?
From left to right, is it increasing?
If you drew a line or curve though the points and extended the the graph in both directions, what would the x and y interprets be if possible?
Are there any values of x or y in which are impossible?
Some additional questions I would add to fully describe a graph would be:
Does the graph have a line or a curve?
Did the graph remain constant, or stay the same?
Was there any sudden increases or decreases?
What was the lowest point in the graph?
What was the highest point on the graph?
What is the x- axis representing?

Functions

An equation is considered a function when it’s input values is associated with only one output value. We see functions almost everyday! An example of a function that we see is a vending machine. To get the candy that you want from the machine, you have to insert a code that indicates which one you want. However, there can be different codes (inputs) for that one candy. Although, there cannot be a specific code that has different candies (outputs).

Scientific Notation

Scientific notation is the process in which scientists use when working with very large numbers to make it easier for them to write it down. However, there are rules for writing numbers in scientific notation. First, the product that is being multiplied by 10 has to be between 1 and 10. So, in order to do this, you must move the decimal as much times needed to have the number apply to that rule. Another rule is that you must multiply that number by 10 to the power of how ever many times you moved the decimal. If you moved it left, it’s negative and right positive. Finally, another rule is that you must write x for the multiplication sign instead of the dot. The difference between 3 to the power of 8 and 3 x 10 to the power of 8 is that 3 to the power of 8 is solved like: 3x3x3x3x3x3x3x3, which equals 36. But, 3×10 to the power of eight is a solved like: 3x10x10x10x10x10x10x10x10, which equals 300,000,000.

    Simplifying Expressions

To simplify an expression that is asking you to multiply numbers with exponents, for example, 3 squared times 3 to the power of 5, you must add the exponents. Remember, YOU ONLY ADD THE EXPONENTS IF THE BASES ARE THE SAME!!! After you add the exponents, that becomes your new exponent for the same base, in this case 3. So my answer would be 3 to the power of 7. If you have a division problem, like 5 to the power of 8 divided by 5 to the power of 4, you subtract the exponents. AGAIN, ONLY IF THE BASES ARE THE SAME! In this case, the exponents are 8 and 4, so you will end up with 5 to the power of 4.