math ch13: analyzing graphs of functions and relations

the graph of f is the graph of the equation

the value of the function is the directed —— of the graph from the point —— on the ——-

the input values (x values) correspond to the

the output values (y values) correspond to the

the point at which the graph of the function crosses the s axis

to find x intercepts:

is the point at which the graph of the function across the y axis

to find the y intercept:

at x intercept:

at y intercept:

functions that are symmetric with respect to the y axis. this is called the

in even functions, f(-x)=

functions that are symmetric with respect to the origin are called

in odd functions, f(-x)=

f(-x) = f(x) if f(x) is equal to:

f(-x) = -f(x) if f(x) is equal to

if for any two points on an interval, a positive change in x results in a positive change in y. this means the function f is

if for any two points on an interval, a positive change in x results in a negative change in y. this means the function f is

if for any two points on an interval, a positive change in x results in a zero change in y. this means the function is

the greatest value f(x) can attain on some interval of the domain is called the

if the relative maximum is the greatest value a function f can attain over its entire domain, then it is the

the least value f(x) can attain on some interval of the domain is called

if the relative minimum is the least value a function can attain over its entire domain, then its is the

the slope of the line through two points is called

the slope of the secant line is denoted as

the average rate of change on the interval (x1,x2) is

a group of functions with graphs that display one or more similar characterisrics

the simplest function in the family that transformed to create other numbers in a family of functions is called

a constant function has a form of

the graph of a constant function is a

when c=0 in a constant function, f(x) is the

the function f(x)=x passes through

the absolute function is denoted f(x) = I x I and is shaped as a

the quadratic function f(x)=x² is a

the cubic function f(x)=x³ is

the square root function has the form

the cubic root function has the form

the reciprocal function has the form

a positive or negative movement up or down outside the function is called a

translation up K units is represented as

translation down K units is represented as

a translation left or right is positive and inside the function and it is called

translation right h units:

translation left h units

reflections in the x axis is represented as

reflections in the y axis is represented as

the process of modifying a functions graph by applying the ———- to its input our output, resulting in —— that create ——- or

the absolute valye is applied to the input (x) —> the transformation reflects the graph over the

the absolute value is applied to the output (y)—> so the transformation reflects the parts of the graoh below the x axis —-