Functions Flashcards
Dependent variable
Is almost always the vertical axis, y-axis, and is represented as y in equations. Affected by the change if independent variable
Independent variable
This is almost always on the x axis (bottom line of graph) and is represented by x in equations. The variable that changes
What is a relation?
Any set if ordered pairs. A function is a special kind of relation
What is a function?
A relation where there can be only one x-value for each y-value. There can be duplicate y-values but not duplicate x-values in a function.
x-values are called domain
y-values are called range
One-to-one function
When there is only one y-value for each x-value
Vertical line test
A test used to determine if a relation is a function. Pass a straight object like a pencil vertically across the graph, and if it crosses the line of the relation more than once, it is NOT a function
What is basic strategy for solving functions?
Plug in values for x to get values for y. Sometimes a domain, in set brackets, is given and you must find the range.
Ex: given the range {0.2,4} and function rule y = 3x + 2, find the range
y = 3(0) + 2 = 5
y = 3(2) + 2 = 8
y = 3(4) + 2 = 14. Range is {2,8,14}
What is another way of saying “y” in a function?
f(x) read f of x
What real life situations can be modeled with functions?
Situations where the independent and dependent variables increase or decrease together or situations where one increases and the other decreases are often functions
Ex: minutes elapsed in a basketball game vs total points scored
Time candle has been burning vs height of candle
Cost of dinner vs amount if tip at 15%
What is an inverse function?
When the x-values(domain) and y-values(range) are switched. Must be a one to one function.
y = x+3. y^-1 = x^-1 +3
Linear function
Produces a straight line on a graph. Must be one-to-one function. Highest power of x is one
Ex: f(x)= x+8
Non ex= f(x) = x^2 + 8
What are the steps of graphing linear equations from a rule?
- choose at least 3 values, zero and one negative, one positive (-1,0,1)
- Solve for f(x)
- Create table of x and y values
- Plot the points
What is a slope?
Constant rate of change in a linear equation. Change in y divided by change in x. Use delta symbol
How can you tell if there is a constant rate of change when looking at a graph?
If each amount traveled across you travel the same amount up/down to reach the line again. it looks like stair steps.
How do you determine rate if change from a table?
- Find the difference between variables on x side and y side
- Use the equation
