Function Operations Worksheet
Adding & Subtracting Functions
• Independent Practice
Name:
Date:
Period:
Part 1: Combining Functions Algebraically
Show all work and simplify completely
Given functions: \( u(x) = 3x^2 - 2x + 4 \) • \( v(x) = 2x^2 + 5x - 7 \)
#1 Write the function rule for \( w(x) \), if:
\( w(x) = u(x) + v(x) \)
Answer: \( w(x) = \)
#2 Write the function rule for \( w(x) \), if:
\( w(x) = u(x) - v(x) \)
Answer: \( w(x) = \)
#3 Write the function rule for \( w(x) \), if:
\( w(x) = v(x) - u(x) \)
Answer: \( w(x) = \)
Function Operations Practice • Polynomial Combinations Page 1 of 4 • Next →
#4 Determine the values of \( f(x) \), \( g(x) \), and \( h(x) \) to complete the table below:
| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---|
| \( f(x) = 4x - 2 \) | | | | | |
| \( g(x) = 3x \) | | | | | |
| \( h(x) = f(x) + g(x) \) | | | | | |
#5 Determine the values of \( f(x) \), \( g(x) \), and \( h(x) \) to complete the table below:
| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---|
| \( f(x) = 4x - 2 \) | | | | | |
| \( g(x) = 3x \) | | | | | |
| \( h(x) = f(x) - g(x) \) | | | | | |
#6 Determine the values of \( f(x) \), \( g(x) \), and \( h(x) \) to complete the table below:
| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---|
| \( f(x) = 3x^2 - 5 \) | | | | | |
| \( g(x) = -2x \) | | | | | |
| \( h(x) = g(x) - f(x) \) | | | | | |
Function Operations Practice • Horizontal Tables Page 2 of 4 • Next →
For problems #7–9: If \( f(x) = 4x + 1 \) and \( g(x) = x - 3 \)
#7 \( h(x) = f(x) + g(x) \)
| \( x \) | \( f(x) \) | \( g(x) \) | \( h(x) \) |
|---|
| -2 | | | |
| -1 | | | |
| 0 | | | |
| 1 | | | |
| 2 | | | |
Show work:
What is the function for \( h(x) \)?
\( h(x) = \)
#8 \( h(x) = f(x) - g(x) \)
| \( x \) | \( f(x) \) | \( g(x) \) | \( h(x) \) |
|---|
| -2 | | | |
| -1 | | | |
| 0 | | | |
| 1 | | | |
| 2 | | | |
Show work:
What is the function for \( h(x) \)?
\( h(x) = \)
#9 \( h(x) = g(x) - f(x) \)
| \( x \) | \( f(x) \) | \( g(x) \) | \( h(x) \) |
|---|
| -2 | | | |
| -1 | | | |
| 0 | | | |
| 1 | | | |
| 2 | | | |
Show work:
What is the function for \( h(x) \)?
\( h(x) = \)
Function Operations Practice • Vertical Tables & Rules Page 3 of 4 • Next →
Determine each indicated combined function rule. Simplify your answer completely.
#10
If \( f(x) = 6x + 5 \) and \( g(x) = 3x - 4 \), determine \( (f + g)(x) \):
Answer: \( (f + g)(x) = \)
#11
If \( f(x) = 6x + 5 \) and \( g(x) = 3x - 4 \), determine \( (f - g)(x) \):
Answer: \( (f - g)(x) = \)
#12
If \( f(x) = 5x - 3 \) and \( g(x) = 2x + 7 \), determine \( (f + g)(x) \):
Answer: \( (f + g)(x) = \)
#13
If \( f(x) = 5x - 3 \) and \( g(x) = 2x + 7 \), determine \( (g - f)(x) \):
Answer: \( (g - f)(x) = \)
Function Operations Practice • Independent Practice Complete Page 4 of 4
Function Operations Answer Key
Teacher Reference
Function Operations Answer Key
Complete Solutions
Part 1: Combining Functions Algebraically • Solutions
Problems #1–#3
Given functions: \( u(x) = 3x^2 - 2x + 4 \) • \( v(x) = 2x^2 + 5x - 7 \)
#1 \( u(x) + v(x) \)
\( (3x^2 - 2x + 4) \)
\( + (2x^2 + 5x - 7) \)
→ combine like terms
\( w(x) = 5x^2 + 3x - 3 \)
#2 \( u(x) - v(x) \)
\( (3x^2 - 2x + 4) \)
\( - (2x^2 + 5x - 7) \)
→ \( 3x^2 - 2x + 4 - 2x^2 - 5x + 7 \)
\( w(x) = x^2 - 7x + 11 \)
#3 \( v(x) - u(x) \)
\( (2x^2 + 5x - 7) \)
\( - (3x^2 - 2x + 4) \)
→ \( 2x^2 + 5x - 7 - 3x^2 + 2x - 4 \)
\( w(x) = -x^2 + 7x - 11 \)
Part 2: Completed Horizontal Tables of Values
Problems #4–#6
#4 Completed Table: \( h(x) = f(x) + g(x) = 7x - 2 \)
| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---|
| \( f(x) = 4x - 2 \) | -10 | -6 | -2 | 2 | 6 |
| \( g(x) = 3x \) | -6 | -3 | 0 | 3 | 6 |
| \( h(x) = f(x) + g(x) \) | -16 | -9 | -2 | 5 | 12 |
#5 Completed Table: \( h(x) = f(x) - g(x) = x - 2 \)
| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---|
| \( f(x) = 4x - 2 \) | -10 | -6 | -2 | 2 | 6 |
| \( g(x) = 3x \) | -6 | -3 | 0 | 3 | 6 |
| \( h(x) = f(x) - g(x) \) | -4 | -3 | -2 | -1 | 0 |
#6 Completed Table: \( h(x) = g(x) - f(x) = -3x^2 - 2x + 5 \)
| \( x \) | -2 | -1 | 0 | 1 | 2 |
|---|
| \( f(x) = 3x^2 - 5 \) | 7 | -2 |
