9th Grade Math, Unit 2

What are functions?

A mathematical thing. Functions give one output value for one input value. Functions only give one output value for one input value, not multiple output values for one input value.

What are independent and dependent variables?

In linear table, X is independent variable and Y is dependent variable. Input values of a function are the independent variables, the output value is the dependent variable in function.

How are functions notated?

f(x)=x

What is the vertical line test?

A test used to see if a graphed line is a function. Works by drawing a vertical line in a cartesian plane. If the line drawn intersects twice in any point of the line graphed, it is not a function. If it only intersects the line once in any point the line is drawn, it is a function.

What is a rule of function outputs?

For every 1 input, there is one output. There cannot be multiple outputs for one input. In a function, you can have the same output in 2 different inputs however. Just not vice versa.

How do you find what input value is for an output value in a function?

To figure out, for example what the input needs to be to get a output of 4 in a function, simply replace f(x) with 4. For example: F(4)=x*2

What are inverse functions?

Functions that are opposite to each other, where one functions input values are the other functions output values.

How do you find inverse functions?

By replacing the x and y values in a function. (Remember that f(x) literally represents y.) For example. F(x)=2x becomes x=2y

What is a interval?

A gap between two endpoints in a line.

What is the local maximum and minimum in a function?

The turning point in a function. Local maximum is when the function reaches its highest and starts decreasing, Local minimum is when the function reaches its lowest low and starts increasing.

What is true about a function?

A function can have multiple x intercepts, but only one y intercept.

How do you find the x and y intercept in a table that represents a function?

When the input value is 0, its a y intercept. When the output value is 0, it is a x intercept

What is the viewing point?

The visible part of a graph in the cartesian plane.

What are sequences?

A set of ordered numbers. Can be finite or infinite.

What is sequence notation?

written as aₙ where n represents the sequence term number. aₙ when combined represents the term value. In the sequence (5, 7, 9, 11..), if n was equal to 2, it would mean term 2 which is 7, so if n was equal to 2, aₙ would be equal to 7.

How do you graph sequences?

With domains (X values) being the term numbers, and ranges (Y values) being the values of the terms.

What is a recursive sequence?

A sequence where the next value is determined by the function of the previous two values. The Fibonacci sequence was a recursive sequence where any terms value was the past 2 terms combined. The recursive sequence formula is for the Fibonacci sequence is written as a(n) = a(n-2) + a(n-1)

What is recursive formula written in function format?

f(x) = f(n - 2) + f(n - 1) This function only works for terms equal to or greater than 3. Because you need the previous 2 term values for it to work. So you must specifically state only for n >= 3 near the function.

What is a recursive function formula that shows the value of the next term in a sequence?

f(n+1) = f(n) + f(n - 1)

What are Arithmetic sequences?

Mathematical sequences with a common difference between all sequence values. For example in the sequence (2, 4, 6, 8…) the common difference is 2. So to find the next value in a arithmetic sequence you add the common difference to the previous term value.

What are Geometric sequences?

Sequences with a common ratio between 2 consecutive terms. For example in the sequence values (2, 4,) the common ratio was 2. To find the next value of a Geometric sequence multiply the current value with the ratio. To find the common ratio, divide to consecutive terms, for example divide 4 with 2 because 4 is the consecutive term. The answer is 2 and that means the common ratio is 2.

What is a important thing to note about sequences?

Not all sequences have a pattern. Some are just RANDOM!

What is the arithmetic sequence formula?

f(n+1) = f(n) + d. Where d is the common difference. This function only applies to n values greater then or equal to one.

What is the Geometric sequence formula?

geometric sequence is f(n+1) = rf(n). R is the common ratio. This function only applies to n values greater then or equal to one.

Why can we make formulas for geometric and arithmetic sequences?

Because both are types of recursive sequences.

What does f(n) mean?

The current term value in a sequence.