Algebra HW, 4/18

Your task: Rewrite the function $g$ in the form $$ g(x) = \frac{a}{x - h} + k. $$ Graph the function. Describe the graph of $g$ as a transformation of the graph of $f(x) = \frac{a}{x}$.

The method I totally forgot about (since I never learned it in school), but that you're great at, is long division! So, I'm not worried about you being able to solve these problems. But, here are the solutions just in case:

31.

$$ g(x) = \frac{5x - 7}{x - 1} $$

Solution: $$ g(x) = \frac{-2}{x - 1} + 5 $$

Desmos Plot:

32.

$$ g(x) = \frac{6x + 4}{x + 5} $$

Solution: $$ g(x) = \frac{-26}{x + 5} + 6 $$

Desmos Plot:

33.

$$ g(x) = \frac{12x}{x - 5} $$

Solution: $$ g(x) = \frac{60}{x - 5} + 12 $$

Desmos Plot:

34.

$$ g(x) = \frac{8x}{x + 13} $$

Solution: $$ g(x) = \frac{-104}{x + 13} + 8 $$

Desmos Plot:

35.

$$ g(x) = \frac{2x + 3}{x} $$

Solution: $$ g(x) = \frac{3}{x} + 2 $$

Desmos Plot:

36.

$$ g(x) = \frac{4x - 6}{x} $$

Solution: $$ g(x) = \frac{-6}{x} + 4 $$

Desmos Plot:

37.

$$ g(x) = \frac{3x + 11}{x - 3} $$

Solution: $$ g(x) = \frac{20}{x - 3} + 3 $$

Desmos Plot:

38.

$$ g(x) = \frac{7x - 9}{x + 10} $$

Solution: $$ g(x) = \frac{-79}{x + 10} + 7 $$

Desmos Plot: