Find the x and y Intercepts f(x)=1/(x+4)-3

$f (x) = \frac{1}{x + 4} - 3$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{1}{x + 4} - 3$

Solve the equation.

Rewrite the equation as $\frac{1}{x + 4} - 3 = 0$ .

$\frac{1}{x + 4} - 3 = 0$

Add $3$ to both sides of the equation.

$\frac{1}{x + 4} = 3$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 4, 1$

Remove parentheses.

$x + 4, 1$

The LCM of one and any expression is the expression.

$x + 4$

Multiply each term in $\frac{1}{x + 4} = 3$ by $x + 4$ to eliminate the fractions.

Multiply each term in $\frac{1}{x + 4} = 3$ by $x + 4$ .

$\frac{1}{x + 4} (x + 4) = 3 (x + 4)$

Simplify the left side.

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{1}{x + 4} (x + 4) = 3 (x + 4)$

Rewrite the expression.

$1 = 3 (x + 4)$

Simplify the right side.

Apply the distributive property.

$1 = 3 x + 3 \cdot 4$

Multiply $3$ by $4$ .

$1 = 3 x + 12$

Solve the equation.

Rewrite the equation as $3 x + 12 = 1$ .

$3 x + 12 = 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$3 x = 1 - 12$

Subtract $12$ from $1$ .

$3 x = - 11$

Divide each term in $3 x = - 11$ by $3$ and simplify.

Divide each term in $3 x = - 11$ by $3$ .

$\frac{3 x}{3} = \frac{- 11}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 11}{3}$

Divide $x$ by $1$ .

$x = \frac{- 11}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{11}{3}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{11}{3}, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{1}{(0) + 4} - 3$

Solve the equation.

Remove parentheses.

$y = \frac{1}{0 + 4} - 3$

Remove parentheses.

$y = \frac{1}{(0) + 4} - 3$

Simplify $\frac{1}{(0) + 4} - 3$ .

Add $0$ and $4$ .

$y = \frac{1}{4} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{1}{4} - 3 \cdot \frac{4}{4}$

Combine $- 3$ and $\frac{4}{4}$ .

$y = \frac{1}{4} + \frac{- 3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 3$ by $4$ .

$y = \frac{1 - 12}{4}$

Subtract $12$ from $1$ .

$y = \frac{- 11}{4}$

Move the negative in front of the fraction.

$y = - \frac{11}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{11}{4})$

List the intersections.

x-intercept(s): $(- \frac{11}{3}, 0)$

y-intercept(s): $(0, - \frac{11}{4})$

Find the x and y Intercepts f(x)=1/(x+4)-3

Related Questions

Support LCMGCF.com by disabling your adblocker.