Parent Functions

Question 1

Which
parent function
is this?

Answer 1

Linear function

Question 2

Which
parent function
is this?

Answer 2

Absolute value function

Question 3

Which
parent function
is this?

Answer 3

Quadratic function

Question 4

Which
parent function
is this?

Answer 4

Cubic function

Question 5

Which
parent function
is this?

Answer 5

Exponential function

Question 6

Which
parent function
is this?

Answer 6

Logarithmic function

Question 7

Which
parent function
is this?

Answer 7

Square root function

Question 8

Which
parent function
is this?

Answer 8

Cube root function

Question 9

Which
parent function
is this?

Answer 9

Rational function

Question 10

What family of functions
does

f(x) = −2(x + 3) − 1

belong to?

Answer 10

Linear function family

Degree of one.

Question 11

What family of functions
does

f(x) = −2 | x + 3 | − 1

belong to?

Answer 11

Absolute value family

Absolute value symbols.

Question 12

What family of functions
does

f(x) = −2x² + 3x − 1

belong to?

Answer 12

Quadratic family

Degree of two.

Question 13

What family of functions
does

f(x) = 2^−x + 3

belong to?

Answer 13

Exponential family

Variable in exponent.

Question 14

What family of functions
does

f(x) = −1.5 ln(−x + 4) − 1

belong to?

Answer 14

Logarithmic family

Variable in argument.

Question 15

What family of functions
does

f(x) = −(−x + 2)^1/2 − 2

belong to?

Answer 15

Square root family

Could also be written as
f(x) = −√(−x + 2) − 2

Question 16

What family of functions
does

f(x) = −(−x + 2)^1/3 − 2

belong to?

Answer 16

Cube root family

Question 17

What family of functions
does

f(x) = −2x⁻¹ + 3
belong to?

Answer 17

Rational family

Variable in the denominator.

Could also be written as
f(x) = −2 + 3
x

Question 18

What are the
parent function & general form
of the
linear function?

Answer 18

Parent function:

• *y = x**
• (see below)*

General form:
f(x) = ax + b

Question 19

What are the
parent function & general form
of the
absolute value function?

Answer 19

Parent function:

• *y = | x |**
• (see below)*

General form:
f(x) = a | bx + c | + d

Question 20

What are the
parent function & general form
of the
quadratic function?

Answer 20

Parent function:

• *y = x^{<span>2</span>}**
• (see below)*

General form:
f(x) = ax² + bx + c

Question 21

What are the
parent function & general form
of the
cubic function?

Answer 21

Parent function:

• *y = x^{<span>3</span>}**
• (see below)*

General form:
f(x) = ax³ + bx² + cx + d

Question 22

What are the
parent function & general form
of the
exponential function?

Answer 22

Parent function:

• *y = 2^{<span>x</span>}**
• (see below)*

General form:
f(x) = ab^x+c + d

Question 23

What are the
parent function & general form
of the
logarithmic function?

Answer 23

Parent function:

• *y = log x**
• (see below)*

General form:
f(x) = a log (bx + c) + d

Question 24

What are the
parent function & general form
of the
square root function?

Answer 24

Parent function:

• *y = √(x)**
• (see below)*

General form:
f(x) = a √(b(x + c)) + d

All
even roots
will look similar.

Question 25

What are the **_parent function_ & _general form_** of the **cube root function**?

Answer 25

Parent function: * *y = x^1/3** * (see below)* General form: **f(x) = a (bx + c)^1/3 + d** *All _odd roots_ will look similar.*

Question 26

What are the **_parent function_ & _general form_** of the **rational function**?

Answer 26

Parent function: **y = _1_ x** *(see below, a _hyperbola_)* General form: **f(x) = _a_ + d b(x − c)** OR **_f(x)_ g(x)** OR **f(x) = _ax + b_ cx +d**

Question 27

What are some _noteworthy features_ of **f(x) = x**?

Answer 27

Domain: **(−∞, ∞)** Range: **(−∞, ∞)** Asymptotes: **None** End behavior: **As x → −∞, f(x) → −∞ As x → ∞, f(x) → ∞​** * x*-intercept: * *(0, 0)** * y*-intercept: * *(0, 0)** ​Other noteworthy points: ​**(−1, −1) (1, 1)**

Question 28

What are some _noteworthy features_ of **f(x) = | x |**?

Answer 28

Domain: **(−∞, ∞)** Range: **[0, ∞)** Asymptotes: **None** End behavior: **As x → −∞, f(x) → ∞ As x → ∞, f(x) → ∞​** * x*-intercept: * *(0, 0)** * y*-intercept: * *(0, 0)** ​Other noteworthy points: **​(−1, 1) (1, 1)​**

Question 29

What are some _noteworthy features_ of **f(x) = x²**?

Answer 29

Domain: **(−∞, ∞)** Range: **[0, ∞)** Asymptotes: **None** End behavior: **As x → −∞, f(x) → ∞ As x → ∞, f(x) → ∞​** * x*-intercept: * *(0, 0)** * y*-intercept: * *(0, 0)** ​Other noteworthy points: **​(−1, 1) (1, 1)**

Question 30

What are some _noteworthy features_ of **f(x) = x³**?

Answer 30

Domain: **(−∞, ∞)** Range: **(−∞, ∞)** Asymptotes: **None** End behavior: **As x → −∞, f(x) → −∞ As x → ∞, f(x) → ∞​** * x*-intercept: * *(0, 0)** * y*-intercept: * *(0, 0)** ​Other noteworthy points: **​(−1, −1) (1, 1)**

Question 31

What are some _noteworthy features_ of **f(x) = 2^x**?

Answer 31

Domain: **(−∞, ∞)** Range: **(0, ∞)** Asymptotes: _Horizontal asymptote_: **y = 0** End behavior: **As x → −∞, f(x) → 0 As x → ∞, f(x) → ∞​** * x*-intercept: * *None** * y*-intercept: * *(0, 1)** Other noteworthy points: **​(−1, 1/2) (1, 2) (2, 4)**

Question 32

What are some _noteworthy features_ of **f(x) = log x**?

Answer 32

Domain: **(0, ∞)** Range: **(−∞, ∞)** Asymptotes: _Vertical asymptote_: **x = 0** End behavior: **As x → 0, f(x) → −∞ As x → ∞, f(x) → ∞​** * x*-intercept: * *(1, 0)** * y*-intercept: * *None** Other noteworthy points: **(10, 1)** *or: (BASE, 1)*

Question 33

What are some _noteworthy features_ of **f(x) = √(x)**?

Answer 33

Domain: **(0, ∞)** Range: **(0, ∞)** Asymptotes: **None** End behavior: **As x → 0, f(x) → 0 As x → ∞, f(x) → ∞​** * x*-intercept: * *(0, 0)** * y*-intercept: * *(0, 0)** Other noteworthy points: **(1, 1) (4, 2)**

Question 34

What are some _noteworthy features_ of **f(x) = x^1/3**?

Answer 34

Domain: **(−∞, ∞)** Range: **(−∞, ∞)** Asymptotes: **None** End behavior: **As x → −∞, f(x) → −∞ As x → ∞, f(x) → ∞​** * x*-intercept: * *(0, 0)** * y*-intercept: * *(0, 0)** Other noteworthy points: **(−1, −1) (1, 1)​**

Question 35

What are some _noteworthy features_ of * *f(x) = _1_**? * *x**

Answer 35

Domain: **(−∞, ∞), x ≠ 0** Range: **(−∞, ∞), y ≠ 0** Asymptotes: _Horizontal_: **y = 0** _Vertical_: **x = 0** End behavior: **As x → −∞, f(x) → 0⁻ As x → ∞, f(x) → 0⁺​** **As x → 0⁻, f(x) → −∞ As x → 0⁺, f(x) → ∞​** * x*-intercept: * *None** * y*-intercept: * *None** Other noteworthy points: * *(−1, −1)** * *(1, 1)**