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”