Chapter 1 Linear Functions And Change Flashcards
What is a Function?
A rule that takes certain numbers as inputs and assigns to each input number exactly one output number.
What is the dependent and independent variable in this function?
Q = f(t)
Q is the dependent variable
f(t) is the independent variable
Must a function be definable as a formula?
No
When is a relationship not a function?
When an input gives more than one single output
What is the vertical line test?
If there is a vertical line that intersects a graph in more than one point, then the graph does not represent a function
What is the rate of change of a function?
The average rate of change of a given quantity over time
What is the basic formula for the rate of change?
Change in Quantity
—————————-
Change in Time
Find the average rate of change of the formula f(x) = x^2 between the x input of 1 and 3
f(3) - f(1). 9 - 1
————- = ———- = 4
3 - 1. 2
What type of function has a constant rate of change?
Linear function
Formula for linear functions
Output = initial value + Rate of Change x Input
Or
y = b + mx
What is the slope-intercept form?
y = b + mx
What is the Point-Slope Form?
y - Y = m(x - X)
What is the Standard form?
Ax + By + C = 0
What is the slope of a perpendicular line?
m = -1/M
How would you find the intersection between two lines?
To find this, simply take both equations and equal them ( as in have them on either side of the equals symbol )
What will flip the arrow in a linear inequality?
When dividing or multiplying by a negative number to move to the other side
What is Linear Regression?
The process by which one can find the line of best fit to the data
What is interpolation?
Finding a point on the graph that correlates with the given input within a predefined set of input
What is extrapolation?
It is predicting the output of a given input that is outside the given input range and output data on the graph.
