Question

1. $y = 4 + 2^x$

x	y
2
3

1. $y = 2x^3 - 5$

x	y
1
2

1. $y = -2x + 10$

x	y
-2
0

Explanation:

Step1: Solve for \( y = 4 + 2^x \)

Substep 1.1: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 4 + 2^x \). We know that \( 2^1 = 2 \), so \( y = 4 + 2 = 6 \).

Substep 1.2: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 4 + 2^x \). \( 2^2 = 4 \), so \( y = 4 + 4 = 8 \).

Substep 1.3: When \( x = 3 \)

Substitute \( x = 3 \) into \( y = 4 + 2^x \). \( 2^3 = 8 \), so \( y = 4 + 8 = 12 \).

Step2: Solve for \( y = 2x^3 - 5 \)

Substep 2.1: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = 2x^3 - 5 \). \( 2\times0^3 - 5 = 0 - 5 = -5 \).

Substep 2.2: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 2x^3 - 5 \). \( 2\times1^3 - 5 = 2 - 5 = -3 \).

Substep 2.3: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 2x^3 - 5 \). \( 2\times2^3 - 5 = 2\times8 - 5 = 16 - 5 = 11 \).

Step3: Solve for \( y = -2x + 10 \)

Substep 3.1: When \( x = -4 \)

Substitute \( x = -4 \) into \( y = -2x + 10 \). \( -2\times(-4) + 10 = 8 + 10 = 18 \).

Substep 3.2: When \( x = -2 \)

Substitute \( x = -2 \) into \( y = -2x + 10 \). \( -2\times(-2) + 10 = 4 + 10 = 14 \).

Substep 3.3: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = -2x + 10 \). \( -2\times0 + 10 = 0 + 10 = 10 \).

Filled Tables:

For \( y = 4 + 2^x \):

\( x \)	\( y \)
2	8
3	12

For \( y = 2x^3 - 5 \):

\( x \)	\( y \)
1	-3
2	11

For \( y = -2x + 10 \):

\( x \)	\( y \)
-2	14
0	10

Answer:

Step1: Solve for \( y = 4 + 2^x \)

Substep 1.1: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 4 + 2^x \). We know that \( 2^1 = 2 \), so \( y = 4 + 2 = 6 \).

Substep 1.2: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 4 + 2^x \). \( 2^2 = 4 \), so \( y = 4 + 4 = 8 \).

Substep 1.3: When \( x = 3 \)

Substitute \( x = 3 \) into \( y = 4 + 2^x \). \( 2^3 = 8 \), so \( y = 4 + 8 = 12 \).

Step2: Solve for \( y = 2x^3 - 5 \)

Substep 2.1: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = 2x^3 - 5 \). \( 2\times0^3 - 5 = 0 - 5 = -5 \).

Substep 2.2: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 2x^3 - 5 \). \( 2\times1^3 - 5 = 2 - 5 = -3 \).

Substep 2.3: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 2x^3 - 5 \). \( 2\times2^3 - 5 = 2\times8 - 5 = 16 - 5 = 11 \).

Step3: Solve for \( y = -2x + 10 \)

Substep 3.1: When \( x = -4 \)

Substitute \( x = -4 \) into \( y = -2x + 10 \). \( -2\times(-4) + 10 = 8 + 10 = 18 \).

Substep 3.2: When \( x = -2 \)

Substitute \( x = -2 \) into \( y = -2x + 10 \). \( -2\times(-2) + 10 = 4 + 10 = 14 \).

Substep 3.3: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = -2x + 10 \). \( -2\times0 + 10 = 0 + 10 = 10 \).

Filled Tables:

For \( y = 4 + 2^x \):

\( x \)	\( y \)
2	8
3	12

For \( y = 2x^3 - 5 \):

\( x \)	\( y \)
1	-3
2	11

For \( y = -2x + 10 \):

\( x \)	\( y \)
-2	14
0	10