Chapter 2: Functions, Equations, and Graphs Flashcards
What is a relation?
set of input and output values
What are the four ways of showing relation?
ordered pair, mapping diagram, table of values, and a graph
What is the domain?
set of inputs (x-coordinates)
What is the range?
set of outputs (y-coordinates)
What is a function?
a relation were each element of domain corresponds with one element of the range
What tests if a relation is a function?
vertical-line test
What is the vertical line test?
if a vertical line passes through more than one point on a graph then it is NOT a function
What are the ways of writing a function rule in function notation?
- y = 3x + 2
- f(x) = 3x + 2
- f(1) = 3(1) + 2
What is the independent variable
input of the function (represented by x)
What is the dependent variable?
output of the function (represented by f(x) or y)
What is the formula for a direct variation function?
y = kx
What is the constant of variation?
ratio of all output-input pairs (y/x)
Does y vary directly with x in 7y = 14x + 7? If so what is the constant of variation
No; can’t write it in y = kx
What is the slope of a vertical line?
undefined
What is slope-intercept form
y = mx + b
What is point-slope form?
y - y1 = m ( x - x1)
What is standard form?
Ax + By = C (A can NOT be a fraction)
How can you graph a line in standard form
plug in 0 for x to find the y-intercept and vice-versa
What is the slope of parallel lines?
equal
What is the slope of perpendicular lines?
opposite reciprocal (ex. -2 and 1/2)
What is a scatterplot?
graph that relates two sets of data by plotting the data as ordered pairs
What is a correlation?
strength of a relationship
What is a trend line?
approximate line of the related data
What is the line of best fit?
most accurate line of the related data
What are the two types of translations?
vertical and horizontal
How can you show a vertical translation algebraically?
f (x) + k
How can you show a horizontal translation algebraically?
f (x - h)
What does a vertical stretch do?
multiplies all the y-values of a function by a factor greater than one
What does a vertical compression do?
multiplies all the y-values of a function by a fraction between 0 and 1
What formula must a function have be to consider the transformation?
y = a (x - h) + k
What is the shape of a absolute value function?
symmetrical v
What is a linear inequality
inequality in two variable whose graph is regional
How do you test the boundary of a linear inequality?
pick a point not on the boundary and if it true than that region if shaded (all possible solutions of inequality)
