Quiz about Function Notation Transformation

Question 1

Question 1.

Accepted Answer

$$𝑦=𝑓(𝑥+3)$$

Answer

$$𝑦=𝑓(𝑥)+3$$

Answer

$$𝑦=𝑓(𝑥)−3$$

Answer

$$𝑦=𝑓(𝑥−3)$$

Question 2

Question 2.

Accepted Answer

$$𝑦=𝑓(𝑥)+2$$

Answer

$$𝑦=𝑓(𝑥)−2$$

Answer

$$𝑦=𝑓(𝑥+2)$$

Answer

$$𝑦=𝑓(𝑥−2)$$

Question 3

Question 3.

Accepted Answer

$$𝑦=𝑓(2𝑥)$$

Answer

$$𝑦=𝑓(1/2𝑥)$$

Answer

$$𝑦=2𝑓(𝑥)$$

Answer

$$𝑦=1/2𝑓(𝑥)$$

Question 4

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

Accepted Answer

f(x - 3)

Answer

f(x + 3)

Answer

f(x) + 3

Answer

f(x) - 3

Question 5

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

Accepted Answer

-f(x)

Answer

f(-x)

Answer

f-1(x)

Answer

f(2x)

Question 6

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

Accepted Answer

(-6, 5)

Answer

(-2, 5)

Answer

(-4, 3)

Answer

(-4, 7)

Question 7

Question 7.

Accepted Answer

$$𝑦=𝑓(𝑥−2)$$

Answer

$$𝑦=𝑓(𝑥)+2$$

Answer

$$𝑦=𝑓(𝑥)−2$$

Answer

$$𝑦=𝑓(𝑥+2)$$

Question 8

Question 8.

Accepted Answer

$$𝑦=𝑓(𝑥)+2$$

Answer

$$𝑦=𝑓(𝑥)−2$$

Answer

$$𝑦=𝑓(𝑥+2)$$

Answer

$$𝑦=𝑓(𝑥−2)$$

Question 9

Question 9.

Accepted Answer

$$𝑦=𝑓(𝑥)−3$$

Answer

$$𝑦=𝑓(𝑥)+3$$

Answer

$$𝑦=𝑓(𝑥+3)$$

Answer

$$𝑦=𝑓(𝑥−3)$$

Question 10

Question 10.

Accepted Answer

$$𝑦=2𝑓(𝑥)$$

Answer

$$𝑦=𝑓(2𝑥)$$

Answer

$$𝑦=𝑓(1/2𝑥)$$

Answer

$$𝑦=1/2𝑓(𝑥)$$

Question 11

Describe the transformation that occurred

h(x) = 1/5f(x)

Accepted Answer

vertical compression by 5

Answer

vertical stretch by 5

Answer

vertical translation by 5

Answer

vertical translation by -5

Question 12

Which of the following transformations are present (select all that apply)?

Accepted Answer

vertical shift

Accepted Answer

reflection over horizontal axis

Accepted Answer

horizontal compression

Answer

reflection over vertical axis

Answer

Rotation about origin

Question 13

Which of the following transformations are present?
-2f(x - 1) + 2

Accepted Answer

Shift 1 unit right

Answer

Shift 1 unit down

Answer

Shift 1 unit up

Answer

Shift 1 unit left

Question 14

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

Accepted Answer

f(x - 4) + 3

Answer

f(x + 3) - 4

Answer

f(x + 4) + 3

Answer

f(x + 3) + 4

Question 15

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

Accepted Answer

f(x + 2)

Answer

f(x) + 2

Answer

f(x - 2)

Answer

f(x) - 2

Question 16

Describe the transformation of y = f(x) to the new function
y = f(1/5x)

Accepted Answer

Horizontal stretch by a factor of 5

Answer

Horizontal shrink by a factor of 1/5

Answer

Vertical stretch be a factor of 5

Answer

Vertically shrink by a factor of 1/5

Question 17

Choose the correct transformations.

Accepted Answer

horizontal shift to the left 4 and vertical shift down 2

Answer

horizontal shift to the right 4 and vertical shift down 2

Answer

horizontal shift to the left 4 and vertical shift up 2

Answer

horizontal shift to the right 4 and vertical shift up 2

Function Notation Transformation

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