Unit 4 Algebra

Question 1

How do you determine if a function is even?

Answer 1

If f(-x) = f(x)

Question 2

How do you determine if a function is odd?

Answer 2

If f(-x) = -f(x)

Question 3

How do you determine if a function is even nor odd?

Answer 3

If f(x) is not equal to f(-x)
and
If -f(x) is not equal to f(-x)

Question 4

What type of transformation is f(x)+2

Answer 4

Vertical shift 2 units up.

Question 5

What type of transformation is f(x+2)

Answer 5

Horizontal shift 2 units left.

Question 6

What type of transformation is f(2x)

Answer 6

Horizontal compression by a factor of 2.

Question 7

What type of transformation is 2f(x)

Answer 7

Vertical stretch by a factor of 2.

Question 8

How does f(x+2) affect this?
domain [2, 6]
range [4, 8]

Answer 8

Domain [0, 4]
Range [4, 8]

Question 9

How does f(x) + 2 affect this?
domain [2, 6]
range [4, 8]

Answer 9

domain [2, 6]
range [6, 10]

Question 10

How does f(2x) affect this?
domain [2, 6]
range [4, 8]

Answer 10

domain [1, 3]
range [4, 8]

Question 11

How does 2f(x) affect this?
domain [2, 6]
range [4, 8]

Answer 11

domain [2, 6]
range [8, 16]

Question 12

How does -f(x) affect this?
domain [2, 6]
range [4, 8]

Answer 12

domain [2, 6]
range [-8, -4]

Question 13

How does f(-x) affect this?
domain [2, 6]
range [4, 8]

Answer 13

domain [-6, -2]
range [4, 8]

Question 14

How does f(x/2) affect this?
domain [2, 6]
range [4, 8]

Answer 14

domain [4, 12]
range [4, 8]