Graph f(x)=(x^2-3x-4)/(-4x+8)

$f (x) = \frac{x^{2} - 3 x - 4}{- 4 x + 8}$

Find the point at $x = - 1$ .

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = - \frac{((- 1) - 4) ((- 1) + 1)}{4 ((- 1) - 2)}$

Simplify the result.

Simplify the numerator.

Subtract $4$ from $- 1$ .

$f (- 1) = - \frac{- 5 (- 1 + 1)}{4 (- 1 - 2)}$

Add $- 1$ and $1$ .

$f (- 1) = - \frac{- 5 \cdot 0}{4 (- 1 - 2)}$

Simplify the expression.

Subtract $2$ from $- 1$ .

$f (- 1) = - \frac{- 5 \cdot 0}{4 \cdot - 3}$

Multiply $- 5$ by $0$ .

$f (- 1) = - \frac{0}{4 \cdot - 3}$

Multiply $4$ by $- 3$ .

$f (- 1) = - \frac{0}{- 12}$

Divide $0$ by $- 12$ .

$f (- 1) = - 0$

Multiply $- 1$ by $0$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = - \frac{((3) - 4) ((3) + 1)}{4 ((3) - 2)}$

Simplify the result.

Simplify the numerator.

Subtract $4$ from $3$ .

$f (3) = - \frac{- 1 (3 + 1)}{4 (3 - 2)}$

Add $3$ and $1$ .

$f (3) = - \frac{- 1 \cdot 4}{4 (3 - 2)}$

Simplify the expression.

Subtract $2$ from $3$ .

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

Multiply $- 1$ by $4$ .

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

Multiply $4$ by $1$ .

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

Divide $- 4$ by $4$ .

$f (3) = 1$

Multiply $- 1$ by $- 1$ .

$f (3) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Find the point at $x = - 2$ .

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = - \frac{((- 2) - 4) ((- 2) + 1)}{4 ((- 2) - 2)}$

Simplify the result.

Cancel the common factor of $(- 2) - 4$ and $4$ .

Factor $2$ out of $((- 2) - 4) ((- 2) + 1)$ .

$f (- 2) = - \frac{2 ((- 1 - 2) ((- 2) + 1))}{4 ((- 2) - 2)}$

Cancel the common factors.

Factor $2$ out of $4 ((- 2) - 2)$ .

$f (- 2) = - \frac{2 ((- 1 - 2) ((- 2) + 1))}{2 (2 ((- 2) - 2))}$

Cancel the common factor.

$f (- 2) = - \frac{2 ((- 1 - 2) ((- 2) + 1))}{2 (2 ((- 2) - 2))}$

Rewrite the expression.

$f (- 2) = - \frac{(- 1 - 2) ((- 2) + 1)}{2 ((- 2) - 2)}$

Simplify the numerator.

Subtract $2$ from $- 1$ .

$f (- 2) = - \frac{- 3 (- 2 + 1)}{2 (- 2 - 2)}$

Add $- 2$ and $1$ .

$f (- 2) = - \frac{- 3 \cdot - 1}{2 (- 2 - 2)}$

Simplify the expression.

Subtract $2$ from $- 2$ .

$f (- 2) = - \frac{- 3 \cdot - 1}{2 \cdot - 4}$

Multiply $- 3$ by $- 1$ .

$f (- 2) = - \frac{3}{2 \cdot - 4}$

Multiply $2$ by $- 4$ .

$f (- 2) = - \frac{3}{- 8}$

Move the negative in front of the fraction.

$f (- 2) = \frac{3}{8}$

The final answer is $\frac{3}{8}$ .

$\frac{3}{8}$

Convert $\frac{3}{8}$ to decimal.

$y = 0.375$

Find the point at $x = 0$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = - \frac{((0) - 4) ((0) + 1)}{4 ((0) - 2)}$

Simplify the result.

Cancel the common factor of $(0) - 4$ and $4$ .

Factor $4$ out of $((0) - 4) ((0) + 1)$ .

$f (0) = - \frac{4 ((0 - 1) ((0) + 1))}{4 ((0) - 2)}$

Cancel the common factors.

Cancel the common factor.

$f (0) = - \frac{4 ((0 - 1) ((0) + 1))}{4 ((0) - 2)}$

Rewrite the expression.

$f (0) = - \frac{(0 - 1) ((0) + 1)}{(0) - 2}$

Simplify the numerator.

Rewrite $0$ as $- 1 (0)$ .

$f (0) = - \frac{(- 1 \cdot 0 - 1) (0 + 1)}{0 - 2}$

Rewrite $- 1$ as $- 1 (1)$ .

$f (0) = - \frac{(- 1 \cdot 0 - 1 \cdot 1) (0 + 1)}{0 - 2}$

Factor $- 1$ out of $- 1 \cdot 0 - 1 \cdot 1$ .

$f (0) = - \frac{- 1 \cdot ((0 + 1) (0 + 1))}{0 - 2}$

Raise $0 + 1$ to the power of $1$ .

$f (0) = - \frac{- 1 \cdot ((0 + 1) (0 + 1))}{0 - 2}$

Raise $0 + 1$ to the power of $1$ .

$f (0) = - \frac{- 1 \cdot ((0 + 1) (0 + 1))}{0 - 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (0) = - \frac{- 1 \cdot {(0 + 1)}^{1 + 1}}{0 - 2}$

Add $1$ and $1$ .

$f (0) = - \frac{- 1 \cdot {(0 + 1)}^{2}}{0 - 2}$

Subtract $2$ from $0$ .

$f (0) = - \frac{- 1 \cdot {(0 + 1)}^{2}}{- 2}$

Simplify the numerator.

Add $0$ and $1$ .

$f (0) = - \frac{- 1 \cdot 1^{2}}{- 2}$

One to any power is one.

$f (0) = - \frac{- 1 \cdot 1}{- 2}$

Reduce the expression by cancelling the common factors.

Multiply $- 1$ by $1$ .

$f (0) = - \frac{- 1}{- 2}$

Dividing two negative values results in a positive value.

$f (0) = - \frac{1}{2}$

The final answer is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Convert $- \frac{1}{2}$ to decimal.

$y = - 0.5$

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = - \frac{((1) - 4) ((1) + 1)}{4 ((1) - 2)}$

Simplify the result.

Simplify the numerator.

Subtract $4$ from $1$ .

$f (1) = - \frac{- 3 (1 + 1)}{4 (1 - 2)}$

Add $1$ and $1$ .

$f (1) = - \frac{- 3 \cdot 2}{4 (1 - 2)}$

Reduce the expression by cancelling the common factors.

Subtract $2$ from $1$ .

$f (1) = - \frac{- 3 \cdot 2}{4 \cdot - 1}$

Multiply.

Multiply $- 3$ by $2$ .

$f (1) = - \frac{- 6}{4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$f (1) = - \frac{- 6}{- 4}$

Cancel the common factor of $- 6$ and $- 4$ .

Factor $- 2$ out of $- 6$ .

$f (1) = - \frac{- 2 \cdot 3}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$f (1) = - \frac{- 2 \cdot 3}{- 2 \cdot 2}$

Cancel the common factor.

$f (1) = - \frac{- 2 \cdot 3}{- 2 \cdot 2}$

Rewrite the expression.

$f (1) = - \frac{3}{2}$

The final answer is $- \frac{3}{2}$ .

$- \frac{3}{2}$

Convert $- \frac{3}{2}$ to decimal.

$y = - 1.5$

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 2 & 0.375 \\ - 1 & 0 \\ 0 & - 0.5 \\ 1 & - 1.5 \\ 3 & 1 \end{array}$

The cubic function can be graphed using the function behavior and the selected points.

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & 0.375 \\ - 1 & 0 \\ 0 & - 0.5 \\ 1 & - 1.5 \\ 3 & 1 \end{array}$

Graph f(x)=(x^2-3x-4)/(-4x+8)

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