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

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

Step 1

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

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

Subtract $3$ from both sides of the equation.

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

Move the negative in front of the fraction.

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

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 $x - 4$ .

Move the leading negative in $- \frac{1}{x - 4}$ into the numerator.

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

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 $- 1$ .

$- 3 x = - 13$

Divide each term in $- 3 x = - 13$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 13$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 13}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 13}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 13}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{13}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{13}{3}, 0)$

Step 2

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

Simplify each term.

Subtract $4$ from $0$ .

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

Dividing two negative values results in a positive value.

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

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 $4$ .

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

Add $1$ and $12$ .

$y = \frac{13}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{13}{4})$

Step 3

List the intersections.

x-intercept(s): $(\frac{13}{3}, 0)$

y-intercept(s): $(0, \frac{13}{4})$

Step 4

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

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