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