Pre Cal: Unit 2
Select the name of the parent function f(x) = cos x
Cosine Function
Select the name of the parent function f(x) = x3
Cubic Function
Select the name of the parent function f(x) = Ax
Exponential Function
Select the name of the parent function f(x) = x
Linear Function
Select the name of the parent function f(x) = x2
Quadratic Function
Select the name of the parent function f(x) = 1/x
Reciprocal Function
Select the name of the parent function f(x) = sin x
Sine Function
Select the name of the parent function f(x)=√x
Square Root Function
limit
a boundary
set
a collection of objects or numbers
function
a description of a variable so closely related to another variable that its value is determined by the other
inverse function
a function derived from another function by switching the independent variable x with the dependent variable y
composite function
a function that results from the combination of two given functions
piecewise function
a function whose resulting graph is produced by two or more intervals
dependent variable
a variable in a function whose value is determined by an independent variable
independent variable
a variable whose value determines the value of another variable
The point where a line touches or crosses an axis is called a(n) ____________
intercept
Two important critical points on a graph are the minimum and _______________ points
maximum
transform
modify a graph by placing a value in its parent functional notation
f(2x) performs what transformation on f(x) ?
narrows f(x)
Identify if the following function is even or odd by its table of values f(x) = x
no odd
f(x)=|x| Do values with opposite sign have the same answer? Is the function even or odd?
no odd
f(x)=x f(x)=f(−x) f(−x)=−f(x)
no yes even
f(x)=x Is the graph symmetrical about the y-axis? Is the graph symmetrical as it relates to the origin? Is the function even or odd?
no yes odd
unique
one of a kind and not duplicated
A function whose resulting graph is produced from two or more intervals is a ____________.
piecewise function
FOIL method
process used in algebra to multiply two binomials together
−f(x) performs what transformation on f(x)
reflects f(x) across the x-axis
f(−x) performs what transformations on f(x)
reflects f(x) across the y-axis
range
results dependent on applying the domain values in a function
f(x)−a is f(x) _______________.
shifted downward
f(x+a) is f(x) ________________.
shifted to the left
f(x−a)is f(x) _______________
shifted to the right
f(x)+a is f(x) _______________.
shifted upward
interval
the distance between two specified points
intercept
the point where a line or curve touches or crosses an axis
symbolically
used as a symbol for words
domain
values of the independent variables of a function
The name of the test to determine if a graph is a function is called the _________
vertical line
f(x)=|x| Is the graph symmetrical about the y-axis? Is the graph symmetrical as it relates to the origin? Is the function even or odd?
yes no even
f(x)=|x| f(x)=f(−x) f(−x)=−f(x) Is the function even or odd?
yes no even/odd
Choose the distance and direction the graph of the function will move f(x)=x2→f(x)=x2+3
3 units upward
Choose the distance and direction the graph of the function will move f(x)=x2→f(x)=x2−4
4 units downward
Choose the distance and direction the graph of the function will move f(x)=x2→f(x)=(x−5)2
5 units to the right
Choose the distance and direction the graph of the function will move f(x)=x2→f(x)=(x+7)2
7 units to the left
Select the piecewise functions
Absolute Value Function Reciprocal Function Greatest Integer Function
|f(x)| will produce a graph __________ the x-axis
above
odd
an expression that has different results from the input of the same number with a positive or a negative sign
even
an expression that has the same results from the input of the same number with a positive or a negative sign
A graph of a function _________________
can cross the y-axis only once
symmetry
condition achieved when two parts of an object divided by a line are reflective and identical
interconnected
connected between each other
The place where a graph turns is called a _________________ point
critical
An interval is the ________________ between two specified points
distance
Which function produces the graph with the most narrow shape?
f(x)=(3x)2
Which function produces the graph with the most narrow shape?
f(x)=(5x)2
Which function produces the graph with the most narrow shape?
f(x)=5x2
A description of a variable so closely related to another variable that its value is determined by the other is a _____________.
function
Check the three ways used to identify a function as being even or odd.
functional notation graphically table of values