Function Notation Partner Quotable Activity - Engage students with differentiated worksheets for collaborative learning and problem-solving.

Here are the step-by-step solutions for the problems shown on the worksheets.

Worksheet A (Left Side)

Functions given:
* $f(x) = 3x + 12$
* $g(x) = x^2 - 1$
* $h(x) = -x + 6$
* $j(x) = -4x^2$
* $k(x) = x^2 + 5x + 1$

Solutions:

1. Find $f(3)$:
Substitute $3$ for $x$ in $f(x)$.
$f(3) = 3(3) + 12 = 9 + 12 = \mathbf{21}$

2. Find $j(-1)$:
Substitute $-1$ for $x$ in $j(x)$.
$j(-1) = -4(-1)^2 = -4(1) = \mathbf{-4}$

3. Find $g(7)$:
Substitute $7$ for $x$ in $g(x)$.
$g(7) = (7)^2 - 1 = 49 - 1 = \mathbf{48}$

9. Find $f(-2)$:
Substitute $-2$ for $x$ in $f(x)$.
$f(-2) = 3(-2) + 12 = -6 + 12 = \mathbf{6}$

10. Find $g(5)$:
Substitute $5$ for $x$ in $g(x)$.
$g(5) = (5)^2 - 1 = 25 - 1 = \mathbf{24}$

11. Find $h(14)$:
Substitute $14$ for $x$ in $h(x)$.
$h(14) = -(14) + 6 = -14 + 6 = \mathbf{-8}$

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Worksheet B (Right Side)

Functions given:
* $f(x) = x^2 + 3$
* $g(x) = -2x^2$
* $h(x) = 4x - 15$
* $j(x) = x^2 + 3x - 4$
* $k(x) = -x + 4$

Solutions:

1. Find $h(3)$:
Substitute $3$ for $x$ in $h(x)$.
$h(3) = 4(3) - 15 = 12 - 15 = \mathbf{-3}$

2. Find $g(3)$:
Substitute $3$ for $x$ in $g(x)$.
$g(3) = -2(3)^2 = -2(9) = \mathbf{-18}$

3. Find $f(4)$:
Substitute $4$ for $x$ in $f(x)$.
$f(4) = (4)^2 + 3 = 16 + 3 = \mathbf{19}$

9. Find $h(6)$:
Substitute $6$ for $x$ in $h(x)$.
$h(6) = 4(6) - 15 = 24 - 15 = \mathbf{9}$

10. Find $g(4)$:
Substitute $4$ for $x$ in $g(x)$.
$g(4) = -2(4)^2 = -2(16) = \mathbf{-32}$

11. Find $f(-5)$:
Substitute $-5$ for $x$ in $f(x)$.
$f(-5) = (-5)^2 + 3 = 25 + 3 = \mathbf{28}$

12. Find $h(-4)$:
Substitute $-4$ for $x$ in $h(x)$.
$h(-4) = 4(-4) - 15 = -16 - 15 = \mathbf{-31}$

13. Find $k(11)$:
Substitute $11$ for $x$ in $k(x)$.
$k(11) = -(11) + 4 = -11 + 4 = \mathbf{-7}$

14. Find $f(6)$:
Substitute $6$ for $x$ in $f(x)$.
$f(6) = (6)^2 + 3 = 36 + 3 = \mathbf{39}$

15. Find $j(-3)$:
Substitute $-3$ for $x$ in $j(x)$.
$j(-3) = (-3)^2 + 3(-3) - 4$
$= 9 - 9 - 4$
$= 0 - 4 = \mathbf{-4}$

16. Find $k(12)$:
Substitute $12$ for $x$ in $k(x)$.
$k(12) = -(12) + 4 = -12 + 4 = \mathbf{-8}$

Final Answer:
Worksheet A Answers:
1. 21
2. -4
3. 48
9. 6
10. 24
11. -8

Worksheet B Answers:
1. -3
2. -18
3. 19
9. 9
10. -32
11. 28
12. -31
13. -7
14. 39
15. -4
16. -8