Graph f(x)=(3x^2-3x-60)/(h(x))

$f (x) = \frac{3 x^{2} - 3 x - 60}{h (x)}$

Find the point at $x = - 2$ .

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

$f (- 2) = \frac{3 ((- 2) - 5) ((- 2) + 4)}{h (- 2)}$

Simplify the result.

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

Factor $2$ out of $3 ((- 2) - 5) ((- 2) + 4)$ .

$f (- 2) = \frac{2 (3 ((- 2) - 5) (- 1 + 2))}{h (- 2)}$

Cancel the common factors.

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

$f (- 2) = \frac{2 (3 ((- 2) - 5) (- 1 + 2))}{2 (h \cdot (- 1))}$

Cancel the common factor.

$f (- 2) = \frac{2 (3 ((- 2) - 5) (- 1 + 2))}{2 (h \cdot (- 1))}$

Rewrite the expression.

$f (- 2) = \frac{3 ((- 2) - 5) (- 1 + 2)}{h \cdot (- 1)}$

Simplify the numerator.

Subtract $5$ from $- 2$ .

$f (- 2) = \frac{3 \cdot (- 7 (- 1 + 2))}{h \cdot (- 1)}$

Multiply $3$ by $- 7$ .

$f (- 2) = \frac{- 21 (- 1 + 2)}{h \cdot (- 1)}$

Add $- 1$ and $2$ .

$f (- 2) = \frac{- 21 \cdot 1}{h \cdot (- 1)}$

Reduce the expression by cancelling the common factors.

Multiply $- 21$ by $1$ .

$f (- 2) = \frac{- 21}{h \cdot (- 1)}$

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

$f (- 2) = \frac{- 21}{- 1 \cdot h}$

Dividing two negative values results in a positive value.

$f (- 2) = \frac{21}{h}$

The final answer is $\frac{21}{h}$ .

$\frac{21}{h}$

Convert $\frac{21}{h}$ to decimal.

$y = \frac{21}{h}$

Find the point at $x = - 1$ .

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

$f (- 1) = \frac{3 ((- 1) - 5) ((- 1) + 4)}{h (- 1)}$

Simplify the result.

Simplify the numerator.

Subtract $5$ from $- 1$ .

$f (- 1) = \frac{3 \cdot (- 6 (- 1 + 4))}{h (- 1)}$

Multiply $3$ by $- 6$ .

$f (- 1) = \frac{- 18 (- 1 + 4)}{h (- 1)}$

Add $- 1$ and $4$ .

$f (- 1) = \frac{- 18 \cdot 3}{h (- 1)}$

Reduce the expression by cancelling the common factors.

Multiply $- 18$ by $3$ .

$f (- 1) = \frac{- 54}{h (- 1)}$

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

$f (- 1) = \frac{- 54}{- 1 h}$

Dividing two negative values results in a positive value.

$f (- 1) = \frac{54}{h}$

The final answer is $\frac{54}{h}$ .

$\frac{54}{h}$

Convert $\frac{54}{h}$ to decimal.

$y = \frac{54}{h}$

Find the point at $x = 1$ .

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

$f (1) = \frac{3 ((1) - 5) ((1) + 4)}{h (1)}$

Simplify the result.

Simplify the numerator.

Subtract $5$ from $1$ .

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

Multiply $3$ by $- 4$ .

$f (1) = \frac{- 12 (1 + 4)}{h (1)}$

Add $1$ and $4$ .

$f (1) = \frac{- 12 \cdot 5}{h (1)}$

Simplify the expression.

Multiply $h$ by $1$ .

$f (1) = \frac{- 12 \cdot 5}{h}$

Multiply $- 12$ by $5$ .

$f (1) = \frac{- 60}{h}$

Move the negative in front of the fraction.

$f (1) = - \frac{60}{h}$

The final answer is $- \frac{60}{h}$ .

$- \frac{60}{h}$

Convert $- \frac{60}{h}$ to decimal.

$y = - \frac{60}{h}$

Find the point at $x = 2$ .

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

$f (2) = \frac{3 ((2) - 5) ((2) + 4)}{h (2)}$

Simplify the result.

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

Factor $2$ out of $3 ((2) - 5) ((2) + 4)$ .

$f (2) = \frac{2 (3 ((2) - 5) (1 + 2))}{h (2)}$

Cancel the common factors.

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

$f (2) = \frac{2 (3 ((2) - 5) (1 + 2))}{2 h}$

Cancel the common factor.

$f (2) = \frac{2 (3 ((2) - 5) (1 + 2))}{2 h}$

Rewrite the expression.

$f (2) = \frac{3 ((2) - 5) (1 + 2)}{h}$

Simplify the numerator.

Subtract $5$ from $2$ .

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

Multiply $3$ by $- 3$ .

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

Add $1$ and $2$ .

$f (2) = \frac{- 9 \cdot 3}{h}$

Simplify the expression.

Multiply $- 9$ by $3$ .

$f (2) = \frac{- 27}{h}$

Move the negative in front of the fraction.

$f (2) = - \frac{27}{h}$

The final answer is $- \frac{27}{h}$ .

$- \frac{27}{h}$

Convert $- \frac{27}{h}$ to decimal.

$y = - \frac{27}{h}$

Find the point at $x = 3$ .

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

$f (3) = \frac{3 ((3) - 5) ((3) + 4)}{h (3)}$

Simplify the result.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$f (3) = \frac{((3) - 5) ((3) + 4)}{h}$

Simplify the numerator.

Subtract $5$ from $3$ .

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

Add $3$ and $4$ .

$f (3) = \frac{- 2 \cdot 7}{h}$

Simplify the expression.

Multiply $- 2$ by $7$ .

$f (3) = \frac{- 14}{h}$

Move the negative in front of the fraction.

$f (3) = - \frac{14}{h}$

The final answer is $- \frac{14}{h}$ .

$- \frac{14}{h}$

Convert $- \frac{14}{h}$ to decimal.

$y = - \frac{14}{h}$

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

$\begin{array}{c} x & y \\ - 2 & \frac{21}{h} \\ - 1 & \frac{54}{h} \\ 1 & - \frac{60}{h} \\ 2 & - \frac{27}{h} \\ 3 & - \frac{14}{h} \end{array}$

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

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & \frac{21}{h} \\ - 1 & \frac{54}{h} \\ 1 & - \frac{60}{h} \\ 2 & - \frac{27}{h} \\ 3 & - \frac{14}{h} \end{array}$

Graph f(x)=(3x^2-3x-60)/(h(x))

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