Quizizz worksheet on operations with functions, including addition, subtraction, and multiplication of functions.

Problem Analysis

The task involves performing operations on functions, specifically addition, subtraction, and multiplication. We are given the following functions:
- \( f(x) = 2x - 2 \)
- \( g(x) = x + 1 \)
- \( h(x) = x^2 \)
- \( j(x) = x^2 - 3x - 4 \)
- \( k(x) = x^2 - 4 \)

We need to solve four problems involving these functions.

---

Problem 1: Find \( (h + f)(x) \)

#### Step 1: Recall the definition of function addition
The sum of two functions \( h(x) \) and \( f(x) \) is defined as:
\[
(h + f)(x) = h(x) + f(x)
\]

#### Step 2: Substitute the given functions
\[
h(x) = x^2 \quad \text{and} \quad f(x) = 2x - 2
\]
\[
(h + f)(x) = h(x) + f(x) = x^2 + (2x - 2)
\]

#### Step 3: Simplify the expression
\[
(h + f)(x) = x^2 + 2x - 2
\]

#### Final Answer for Problem 1:
\[
\boxed{C}
\]

---

Problem 2: Find \( (k - h)(x) \)

#### Step 1: Recall the definition of function subtraction
The difference of two functions \( k(x) \) and \( h(x) \) is defined as:
\[
(k - h)(x) = k(x) - h(x)
\]

#### Step 2: Substitute the given functions
\[
k(x) = x^2 - 4 \quad \text{and} \quad h(x) = x^2
\]
\[
(k - h)(x) = k(x) - h(x) = (x^2 - 4) - x^2
\]

#### Step 3: Simplify the expression
\[
(k - h)(x) = x^2 - 4 - x^2 = -4
\]

#### Final Answer for Problem 2:
\[
\boxed{C}
\]

---

Problem 3: Find \( (h \cdot f)(x) \)

#### Step 1: Recall the definition of function multiplication
The product of two functions \( h(x) \) and \( f(x) \) is defined as:
\[
(h \cdot f)(x) = h(x) \cdot f(x)
\]

#### Step 2: Substitute the given functions
\[
h(x) = x^2 \quad \text{and} \quad f(x) = 2x - 2
\]
\[
(h \cdot f)(x) = h(x) \cdot f(x) = x^2 \cdot (2x - 2)
\]

#### Step 3: Distribute \( x^2 \) across the terms in \( 2x - 2 \)
\[
(h \cdot f)(x) = x^2 \cdot 2x - x^2 \cdot 2 = 2x^3 - 2x^2
\]

#### Final Answer for Problem 3:
\[
\boxed{B}
\]

---

Problem 4: Find \( (j - g)(x) \)

#### Step 1: Recall the definition of function subtraction
The difference of two functions \( j(x) \) and \( g(x) \) is defined as:
\[
(j - g)(x) = j(x) - g(x)
\]

#### Step 2: Substitute the given functions
\[
j(x) = x^2 - 3x - 4 \quad \text{and} \quad g(x) = x + 1
\]
\[
(j - g)(x) = j(x) - g(x) = (x^2 - 3x - 4) - (x + 1)
\]

#### Step 3: Simplify the expression
Distribute the negative sign through the second term:
\[
(j - g)(x) = x^2 - 3x - 4 - x - 1
\]
Combine like terms:
\[
(j - g)(x) = x^2 - 4x - 5
\]

#### Final Answer for Problem 4:
\[
\boxed{C}
\]

---

Final Answers

1. \( \boxed{C} \)
2. \( \boxed{C} \)
3. \( \boxed{B} \)
4. \( \boxed{C} \)