Unit 1: Functions and their Inverses
average rate of change
The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph. Think SLOPE!
step/floor function
function that increases or decreases abruptly from one constant value to another.
symmetry
one shape becomes exactly like another when you move it in some way: turn, flip or slide.
reflection
transformation that maps a point to its mirror image. With functions the line of reflections is the x-axis (y=0)
function notation
using "f(x)=" to represent "y=" ex: f(x)=x² is the same as y = x²
end behavior
A description of the values of the function as x approaches infinity or negative infinity
interval of decrease
A function is decreasing, if as x increases (reading from left to right), y decreases.
interval of increase
A function is increasing, if as x increases (reading from left to right), y also increases .
piecewise function
A function with two or more equations each with a specific domain.
discontinuity (holes)
A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero
domain
All possible input values (x values)
range
All possible output values (y values)
intercepts/zeros
Also known as a solution. Where f(x) = 0. Also known as x-intercepts and roots.
inverse
An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
function
Each input can only have one ouput! Formally: A rule that assigns to each number x in the function's domain a unique number f( )x .
vertical line test
If a vertical line passes through two or more points on the graph, then the relation is NOT a function.
transformation
a change made to a figure or function
conjunction
a compound inequality that contains the word "and"
disjunction
a compound inequality that contains the word "or"
absolute value function
a function in the form of f(x) = |x|
continuous function
a function whose graph is an unbroken line or smooth curve
translation
a horizontal or vertical shift of a function
relative maximum/minimum
a point on the graph of a function that is higher/lower than the nearby points of the graph. Where the graph changes from increasing to decreasing or decreasing to increasing.
absolute maximum/minimum
a point where the function obtains its greatest/least possible value.
relation
a set of ordered pairs (can be represented as an equation, graph, table or mapping)
compression
a transformation that decreases the distance between the points of a graph
stretch
a transformation that increases the distance between the points of a graph
interval notation
a way of writing the set of all real numbers between two endpoints, the symbols [ ] are used to include an endpoint in an interval, and the symbols ( ) are used to exclude an endpoint from an interval; example [4, 8) is the same a 4≤x<8