Math Problem Statement

Answer questions 1 through 18

Answer questions 1 through 18

Solution

Here are the solutions for questions 1 through 18:

  1. f(x)=4x3f(x) = -4x - 3, find f(2)f(-2):
    f(2)=4(2)3=83=5f(-2) = -4(-2) - 3 = 8 - 3 = 5

  2. f(x)=3xf(x) = 3x, find f(1)f(-1):
    f(1)=3(1)=3f(-1) = 3(-1) = -3

  3. f(x)=4x+2f(x) = -4x + 2, find f(1)f(-1):
    f(1)=4(1)+2=4+2=6f(-1) = -4(-1) + 2 = 4 + 2 = 6

  4. f(x)=x+5f(x) = -x + 5, find f(6)f(6):
    f(6)=6+5=1f(6) = -6 + 5 = -1

  5. f(x)=x210x+21f(x) = x^2 - 10x + 21, find f(4)f(4):
    f(4)=4210(4)+21=1640+21=3f(4) = 4^2 - 10(4) + 21 = 16 - 40 + 21 = -3

  6. f(x)=4x6f(x) = -4x - 6, find f(0)f(0):
    f(0)=4(0)6=6f(0) = -4(0) - 6 = -6

  7. f(x)=x26x+3f(x) = x^2 - 6x + 3, find f(2)f(2):
    f(2)=226(2)+3=412+3=5f(2) = 2^2 - 6(2) + 3 = 4 - 12 + 3 = -5

  8. f(x)=x+4f(x) = -x + 4, find f(6)f(6):
    f(6)=6+4=2f(6) = -6 + 4 = -2

  9. f(x)=3x4f(x) = 3x - 4, find f(1)f(-1):
    f(1)=3(1)4=34=7f(-1) = 3(-1) - 4 = -3 - 4 = -7

  10. f(x)=x210x+24f(x) = x^2 - 10x + 24, find f(7)f(7):
    f(7)=7210(7)+24=4970+24=3f(7) = 7^2 - 10(7) + 24 = 49 - 70 + 24 = 3

  11. f(x)=2x5f(x) = -2x - 5, find f(5)f(5):
    f(5)=2(5)5=105=15f(5) = -2(5) - 5 = -10 - 5 = -15

  12. f(x)=4x+1f(x) = -4x + 1, find f(0)f(0):
    f(0)=4(0)+1=1f(0) = -4(0) + 1 = 1

  13. f(x)=3x+2f(x) = -3x + 2, find f(2)f(-2):
    f(2)=3(2)+2=6+2=8f(-2) = -3(-2) + 2 = 6 + 2 = 8

  14. f(x)=3x1f(x) = -3x - 1, find f(0)f(0):
    f(0)=3(0)1=1f(0) = -3(0) - 1 = -1

  15. f(x)=4x1f(x) = -4x - 1, find f(2)f(-2):
    f(2)=4(2)1=81=7f(-2) = -4(-2) - 1 = 8 - 1 = 7

  16. f(x)=x28x+16f(x) = x^2 - 8x + 16, find f(2)f(2):
    f(2)=228(2)+16=416+16=4f(2) = 2^2 - 8(2) + 16 = 4 - 16 + 16 = 4

  17. f(x)=4x4f(x) = -4x - 4, find f(1)f(-1):
    f(1)=4(1)4=44=0f(-1) = -4(-1) - 4 = 4 - 4 = 0

  18. f(x)=2x4f(x) = 2x - 4, find f(2)f(-2):
    f(2)=2(2)4=44=8f(-2) = 2(-2) - 4 = -4 - 4 = -8

Would you like a breakdown of any of these solutions?

Here are five related questions to deepen your understanding:

  1. How do you determine if a function is linear or quadratic?
  2. What happens when you substitute a negative number into a function with an exponent?
  3. How do you solve functions with fractions?
  4. How do you graph quadratic functions from an equation?
  5. What is function notation, and why is it useful?

Tip: Always double-check your substitution to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Evaluating Functions
Linear Functions
Quadratic Functions

Formulas

Linear function: f(x) = ax + b
Quadratic function: f(x) = ax^2 + bx + c

Theorems

Function notation and evaluation

Suitable Grade Level

Grade 8-10