Advanced SAT Math Function Transformations and Multi-Step Problems (Hard)

First, calculate the increase in the function output due to the increase in \( x \). The increase is \( \\frac{2}{3} \\times 30 = 20 \). Next, square this increase, resulting in \( 20^2 = 400 \). Finally, subtract 50 from this squared value, resulting in a final result of \( 400 - 50 = 350 \).

First, calculate the increase in the function output due to the increase in \( x \). The increase is \( \\frac{7}{6} \\times 18 = 21 \). Next, square this increase, resulting in a final result of \( 21^2 = 441 \).

First, calculate the increase in the function output due to the increase in \( x \). The increase is \( \\frac{3}{4} \\times 16 = 12 \). Next, divide this increase by 2, resulting in a final result of \( 12 \\div 2 = 6 \).

First, calculate the decrease in the function output due to the decrease in \( x \). The decrease is \( \\frac{4}{5} \\times 15 = 12 \). Next, multiply this decrease by 2, resulting in a final result of \( 12 \\times 2 = 24 \).

First, calculate the increase in the function output due to the increase in \( x \). The increase is \( \\frac{5}{3} \\times 6 = 10 \). Next, add 15 to this increase, resulting in a final increase of \( 10 + 15 = 25 \).

The increase in the modified quantity is determined by multiplying the temperature increase by \( \\frac{2}{5} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in the modified quantity is \( \\frac{2}{5} \\times 10 = 4 \).

The decrease in the adjusted value is determined by multiplying the temperature decrease by \( \\frac{3}{4} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the decrease in the adjusted value is \( \\frac{3}{4} \\times 16 = 12 \).

The increase in the adjusted temperature is determined by multiplying the temperature increase by \( \\frac{1}{2} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in the adjusted temperature is \( \\frac{1}{2} \\times 8 = 4 \).

The increase in Kelvin is determined by multiplying the temperature increase in Celsius by \( \\frac{9}{5} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in Kelvin is \( \\frac{9}{5} \\times 2.75 = 4.95 \).

The decrease in the function value is determined by multiplying the temperature decrease by \( \\frac{4}{3} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the decrease in the function value is \( \\frac{4}{3} \\times 3 = 4 \).

The increase in the function value is determined by multiplying the temperature increase by \( \\frac{5}{2} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in the function value is \( \\frac{5}{2} \\times 4 = 10 \).

The decrease in the function value is determined by multiplying the temperature decrease by \( \\frac{2}{3} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the decrease in the function value is \( \\frac{2}{3} \\times 9 = 6 \).

The increase in the function value is determined by multiplying the temperature increase by \( \\frac{7}{4} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in the function value is \( \\frac{7}{4} \\times 8 = 14 \).

The increase in the function value is determined by multiplying the temperature increase by \( \\frac{3}{2} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in the function value is \( \\frac{3}{2} \\times 6 = 9 \).

The change in degrees Fahrenheit is determined by multiplying the temperature decrease in Celsius by \( \\frac{5}{9} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the decrease in Fahrenheit temperature is \( \\frac{5}{9} \\times 5.40 = 3.00 \).