2.3 Families of Functions, Transformations, and Symmetry

Question 1

a general term for four specific ways to manipulate the shape and/or position of a point, line, or geometric figure

Answer 1

geometric transformation

Question 2

the use of a standard form of a function where a, h, and k are real numbers and “a ≠ 0” that uses the general form of a parent function

Answer 2

algebraic transformation

Question 3

In the equation below, what do a, h, and k stand for with regards to transforming a graph?

Answer 3

horizontally (h)
vertically (k)
stretch (|a| >1)
compress (0 < |a| < 1)
reflection (a < 1)

Question 4

all the transformations of a function with similar graphs

Answer 4

family of functions

Question 5

the graph of any function in the square or quadratic family

Answer 5

parabola

Question 6

moving the graph left or right without changing its shape so that it coincides with another graph

Answer 6

horizontal translation

Question 7

Name this transformation

Answer 7

translation

Question 8

Name this transformation

Answer 8

reflection

Question 9

Name this transformation

Answer 9

rotation

Question 10

Name this tranformation

Answer 10

dilation

Question 11

In the equation below, name the parent function. Then, describe what transformation has occurred?

Answer 11

Square Root Function
Horizontal Shift to the Right 3 units

Question 12

In the equation below, name the parent function. Then, describe what transformation has occurred?

Answer 12

Square Root Function
Horizontal Shift to the Left 5 units

Question 13

In the equation below, name the parent function. Then, describe what transformation has occurred?

Answer 13

Absolute Value Function
Horizontal Shift to the Right 1 unit

Question 14

In the equation below, name the parent function. Then describe what transformation has occurred?

Answer 14

Quadratic
Horizontal Shift to the left 3 units

Question 15

In the equation below, name the parent function. Then describe what transformation has occurred?

Answer 15

Quadratic
Horizontal Shift to the right 2 units

Question 16

a graph that has a mirror image of one another

Answer 16

reflection

Question 17

How do you determine if there is a reflection over the x-axis?

Answer 17

There is a negative in front of the grouping symbol or parent function.

Question 18

How do you determine if there is a reflection over the y-axis?

Answer 18

There is a negative in front of the variable inside a grouping symbol.

Question 19

What kind if transformation is this?

Answer 19

Reflection over the x-axis

Question 20

What kind of transformation is this?

Answer 20

Reflection over the y-axis

Question 21

Name the transformation for the following graph

Answer 21

Reflection over the x-axis

Question 22

Name the transformation for the following graph

Answer 22

Reflection over the y-axis

Question 23

Name the parent function and the transformation that has occurred in the following equation.

Answer 23

Square Root
Reflection over the y-axis

Question 24

Name the parent function and the transformation that has occurred in the following equation.

Answer 24

Absolute Value
Reflection over the x-axis

Question 25

What kind of transformation occurs when

Answer 25

Vertical Stretch by “a”
Horizontal Compression by “1/a”

Question 26

What kind of transformation occurs when

Answer 26

Vertical compression by “a”
Horizontal Stretch by “1/a”

Question 27

_______________________ are defined for POSITIVE value so “a”

Answer 27

Stretching and Shrinking

Question 28

If “a” is ___________________, then a reflection occurs along with stretching and shrinking as long as “a” does not equal 1.

Answer 28

Negative

Question 29

What kind of transformation occurs when

Answer 29

Vertical Translation up k units

Question 30

What kind of transformation occurs when

Answer 30

Vertical Translation down k units

Question 31

What kind of transformation occurs when

Answer 31

Vertical translation down 3 given that the parent function is the square root

Question 32

a transformation that does not change the shape of a graph

Answer 32

rigid transformation

Question 33

a transformation that changed the shape of the graph

Answer 33

nonrigid transformation

Question 34

what are the rigid transformations

Answer 34

translating horizontally
translating vertically
reflections

Question 35

what are the nonrigid transformations

Answer 35

stretching
shrinking

Question 36

What is the order in which transformations should be performed?

Answer 36

Horizontal Translations (h)
Reflecting/stretching/shrinking (a)
Vertical translations (k)

Question 37

What pneumonic device to help remember the order of transformations?

Answer 37

H-A-K

Question 38

What does H-A-K stand for?

Answer 38

Horizontal Translations (h)
Reflecting/stretching/shrinking (a)
Vertical translations (k)

Question 39

Identity Function

Answer 39

Question 40

Slope Intercept

Answer 40

Question 41

Linear Family

Answer 41

a transformation of the identity function where “a” cannot be 0 which can be simplified to a function in slope intercept form

Question 42

Constant Function

Answer 42

a linear function with slope =0 in the form of:

Question 43

What is meant to be symmetric about the y-axis?

Answer 43

Question 44

What is meant to be symmetric about the origin?

Answer 44

Question 45

Another name for symmetric about the y-axis

Answer 45

Even Function

Question 46

Another name for symmetric about the origin

Answer 46

Odd Function

Question 47

How do you test algebraically if a function is even or odd?

Answer 47

Plug in a -x for every x and simplify. If the original function is the result, the function is even. If the opposite of the original function is the result, the function is odd.

Question 48

How do you solve an inequality by graphing?

Answer 48

Set one side to 0.
Graph the function with a x/y table or transformation rules.
If there is a > symbol, find the intervals above the x-axis.
If there is a < symbol, find the intervals below the x-axis.
The answer should be represented in interval notation.