Graph f(x)=(x^2-5x-14)/(q(x))

$f (x) = \frac{x^{2} - 5 x - 14}{q (x)}$

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = \frac{((- 2) - 7) ((- 2) + 2)}{q (- 2)}$

Simplify the result.

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

Factor $2$ out of $((- 2) - 7) ((- 2) + 2)$ .

$f (- 2) = \frac{2 (((- 2) - 7) (- 1 + 1))}{q (- 2)}$

Cancel the common factors.

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

$f (- 2) = \frac{2 (((- 2) - 7) (- 1 + 1))}{2 (q \cdot (- 1))}$

Cancel the common factor.

$f (- 2) = \frac{2 (((- 2) - 7) (- 1 + 1))}{2 (q \cdot (- 1))}$

Rewrite the expression.

$f (- 2) = \frac{((- 2) - 7) (- 1 + 1)}{q \cdot (- 1)}$

Simplify the numerator.

Subtract $7$ from $- 2$ .

$f (- 2) = \frac{- 9 (- 1 + 1)}{q \cdot (- 1)}$

Add $- 1$ and $1$ .

$f (- 2) = \frac{- 9 \cdot 0}{q \cdot (- 1)}$

Simplify the expression.

Multiply $- 9$ by $0$ .

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

Move $- 1$ to the left of $q$ .

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

Divide $0$ by $- 1 \cdot q$ .

$f (- 2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = \frac{((- 1) - 7) ((- 1) + 2)}{q (- 1)}$

Simplify the result.

Simplify the numerator.

Subtract $7$ from $- 1$ .

$f (- 1) = \frac{- 8 (- 1 + 2)}{q (- 1)}$

Add $- 1$ and $2$ .

$f (- 1) = \frac{- 8 \cdot 1}{q (- 1)}$

Reduce the expression by cancelling the common factors.

Multiply $- 8$ by $1$ .

$f (- 1) = \frac{- 8}{q (- 1)}$

Move $- 1$ to the left of $q$ .

$f (- 1) = \frac{- 8}{- 1 q}$

Dividing two negative values results in a positive value.

$f (- 1) = \frac{8}{q}$

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

$\frac{8}{q}$

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

$y = \frac{8}{q}$

Step 3

Find the point at $x = 1$ .

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

$f (1) = \frac{((1) - 7) ((1) + 2)}{q (1)}$

Simplify the result.

Simplify the numerator.

Subtract $7$ from $1$ .

$f (1) = \frac{- 6 (1 + 2)}{q (1)}$

Add $1$ and $2$ .

$f (1) = \frac{- 6 \cdot 3}{q (1)}$

Simplify the expression.

Multiply $q$ by $1$ .

$f (1) = \frac{- 6 \cdot 3}{q}$

Multiply $- 6$ by $3$ .

$f (1) = \frac{- 18}{q}$

Move the negative in front of the fraction.

$f (1) = - \frac{18}{q}$

The final answer is $- \frac{18}{q}$ .

$- \frac{18}{q}$

Convert $- \frac{18}{q}$ to decimal.

$y = - \frac{18}{q}$

Step 4

Find the point at $x = 2$ .

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

$f (2) = \frac{((2) - 7) ((2) + 2)}{q (2)}$

Simplify the result.

Cancel the common factor of $(2) + 2$ and $2$ .

Factor $2$ out of $((2) - 7) ((2) + 2)$ .

$f (2) = \frac{2 (((2) - 7) (1 + 1))}{q (2)}$

Cancel the common factors.

Factor $2$ out of $q (2)$ .

$f (2) = \frac{2 (((2) - 7) (1 + 1))}{2 q}$

Cancel the common factor.

$f (2) = \frac{2 (((2) - 7) (1 + 1))}{2 q}$

Rewrite the expression.

$f (2) = \frac{((2) - 7) (1 + 1)}{q}$

Simplify the numerator.

Subtract $7$ from $2$ .

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

Add $1$ and $1$ .

$f (2) = \frac{- 5 \cdot 2}{q}$

Simplify the expression.

Multiply $- 5$ by $2$ .

$f (2) = \frac{- 10}{q}$

Move the negative in front of the fraction.

$f (2) = - \frac{10}{q}$

The final answer is $- \frac{10}{q}$ .

$- \frac{10}{q}$

Convert $- \frac{10}{q}$ to decimal.

$y = - \frac{10}{q}$

Step 5

Find the point at $x = 3$ .

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

$f (3) = \frac{((3) - 7) ((3) + 2)}{q (3)}$

Simplify the result.

Simplify the numerator.

Subtract $7$ from $3$ .

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

Add $3$ and $2$ .

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

Simplify the expression.

Multiply $- 4$ by $5$ .

$f (3) = \frac{- 20}{q (3)}$

Move $3$ to the left of $q$ .

$f (3) = \frac{- 20}{3 q}$

Move the negative in front of the fraction.

$f (3) = - \frac{20}{3 q}$

The final answer is $- \frac{20}{3 q}$ .

$- \frac{20}{3 q}$

Convert $- \frac{20}{3 q}$ to decimal.

$y = - \frac{20}{3 q}$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & \frac{8}{q} \\ 1 & - \frac{18}{q} \\ 2 & - \frac{10}{q} \\ 3 & - \frac{20}{3 q} \end{array}$

Step 7

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

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & \frac{8}{q} \\ 1 & - \frac{18}{q} \\ 2 & - \frac{10}{q} \\ 3 & - \frac{20}{3 q} \end{array}$

Step 8

Graph f(x)=(x^2-5x-14)/(q(x))

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