Transformations of Graphs

Question 1

What’s a translation in graph transformations?

Answer 1

A shift of the graph’s position, either vertically or horizontally.

Question 2

What’s the name of the transformation property applied on f: f(x) + 2?

Answer 2

A vertical shift/translation up by 2 units.

Question 3

What’s the name of the property that transforms functions by moving them left/right or up/down?

Answer 3

A translation/shift.

Question 4

Where would the graph of f(x) be moved if f(x) - 2?

Answer 4

It would be shifted vertically down by two units.

Question 5

What type of translation is applied on f in f(x-1)?

Answer 5

A horizontal translation to the right by 1 unit.

Question 6

What’s the difference between f(x) + 1 and f(x + 1)?

Answer 6

f(x) + 1 shifts the graph vertically up by 1 unit and f(x + 1) shift the graph horizontally to the left by 1 unit.

Question 7

If I want all the answers of a function to be 2 more than their original value, how would I transform this function? Let f be the function to be transformed.

Answer 7

f(x) + 2.

Question 8

If I want all the input values for a function to be 2 more than what is originally passed in, how would I transform this function? Let f be the function to be transformed.

Answer 8

f(x+2).

Question 9

Let f be a function. What property of transformation must be used to flip f?

Answer 9

Reflection.

Question 10

Let f be a function. How would f’s graph be rotated over the x-axis?

Answer 10

By multiplying the result of f(x) by -1, -f(x).

Question 11

Let f be a function. How would f’s graph be reflected over the y-axis?

Answer 11

By multiplying the input value, x, by negative 1. This produces f(-x).

Question 12

What is vertical stretching/shrinking of a graph?

Answer 12

Vertical stretching/shrinking is the transformation of a graph where all the graph’s points’ y-values are multiplied by a factor.

Question 13

How is a vertical stretch performed on a graph?

Answer 13

By multiplying the y-values of the graph’s points by a factor greater than 1.

Question 14

How is vertical shrinking performed on a graph?

Answer 14

By multiplying the y-values of the graph’s points by a factor between 0 and 1.

Question 15

What is horizontal shrinking/stretching of a graph?

Answer 15

Horizontal shrinking/stretching is when the x values of a graph’s points are multiplied by a factor.

Question 16

How is horizontal stretching of a graph perfomed.

Answer 16

By multiplying the graph’s x values by a factor between 0 and 1.

Question 17

How is horizontal shrinking of a graph perfomed?

Answer 17

By multiplying the graph’s x values by a factor greater than 1.

Question 18

How many transformations does the graph of the function x^2 have: x^2 + 3.

Answer 18

One.

Question 19

How many transformations does the graph of the function x^2 have: (x - 1)^2 + 3.

Answer 19

Two.

Question 20

How many transformations does the graph of the function x^2 have: 1/2(1 + x)^2 + 3.

Answer 20

Three.

Question 21

How many transformations does the graph of the function x^2 have:
1/2(2 + 1/2(x))^2 + 3.

Answer 21

Four.

Question 22

How many transformations does the graph of the function x^2 have:
-1/2(2 + 1/2(x))^2 + 3.

Answer 22

Five.

Question 23

How many transformations does the graph of the function x^2 have:
-1/2(2 - 2x)^2 + 3.

Answer 23

Six.

Question 24

How should the equation of a transformed graph look like?

Answer 24

y = af(b(x \pm c)) + d, where:
a - vertical stretch/shrink factor;
f - the function
x - the function’s input
b - horizontal stretch/shrink factor
c - horizontal translatation factor
d - vertical translation factor.

Question 25

What’s the order of transformations, in regards to the graph’s equation, when transforming a graph?

Answer 25

1. Stretch/Shrink
2. Reflection
3. Shifting