Graph 2g(x)-3

$2 g (x) - 3$

Step 1

Solve for $y$ .

Add $3$ to both sides of the equation.

$2 y x = 3$

Divide each term in $2 y x = 3$ by $2 x$ and simplify.

Divide each term in $2 y x = 3$ by $2 x$ .

$\frac{2 y x}{2 x} = \frac{3}{2 x}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y x}{2 x} = \frac{3}{2 x}$

Rewrite the expression.

$\frac{y x}{x} = \frac{3}{2 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{y x}{x} = \frac{3}{2 x}$

Divide $y$ by $1$ .

$y = \frac{3}{2 x}$

Step 2

Find the asymptotes.

Find where the expression $\frac{3}{2 x}$ is undefined.

$x = 0$

Consider the rational function $R (x) = \frac{a x^{n}}{b x^{m}}$ where $n$ is the degree of the numerator and $m$ is the degree of the denominator.

1. If $n < m$ , then the x-axis, $y = 0$ , is the horizontal asymptote.

2. If $n = m$ , then the horizontal asymptote is the line $y = \frac{a}{b}$ .

3. If $n > m$ , then there is no horizontal asymptote (there is an oblique asymptote).

Find $n$ and $m$ .

$n = 0$

$m = 1$

Since $n < m$ , the x-axis, $y = 0$ , is the horizontal asymptote.

$y = 0$

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes: $x = 0$

Horizontal Asymptotes: $y = 0$

No Oblique Asymptotes

Vertical Asymptotes: $x = 0$

Horizontal Asymptotes: $y = 0$

No Oblique Asymptotes

Step 3