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 )
