Trigonometry Examples

$h (x) = 4 {(x + 5)}^{3} - 7$

Step 1

Find the point at $x = - 7$ .

Tap for more steps...

Step 1.1

Replace the variable $x$ with $- 7$ in the expression.

$f (- 7) = 4 {((- 7) + 5)}^{3} - 7$

Step 1.2

Simplify the result.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Add $- 7$ and $5$ .

$f (- 7) = 4 {(- 2)}^{3} - 7$

Step 1.2.1.2

Raise $- 2$ to the power of $3$ .

$f (- 7) = 4 \cdot - 8 - 7$

Step 1.2.1.3

Multiply $4$ by $- 8$ .

$f (- 7) = - 32 - 7$

Step 1.2.2

Subtract $7$ from $- 32$ .

$f (- 7) = - 39$

Step 1.2.3

The final answer is $- 39$ .

$- 39$

Step 1.3

Convert $- 39$ to decimal.

$y = - 39$

Step 2

Find the point at $x = - 6$ .

Tap for more steps...

Step 2.1

Replace the variable $x$ with $- 6$ in the expression.

$f (- 6) = 4 {((- 6) + 5)}^{3} - 7$

Step 2.2

Simplify the result.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Add $- 6$ and $5$ .

$f (- 6) = 4 {(- 1)}^{3} - 7$

Step 2.2.1.2

Raise $- 1$ to the power of $3$ .

$f (- 6) = 4 \cdot - 1 - 7$

Step 2.2.1.3

Multiply $4$ by $- 1$ .

$f (- 6) = - 4 - 7$

Step 2.2.2

Subtract $7$ from $- 4$ .

$f (- 6) = - 11$

Step 2.2.3

The final answer is $- 11$ .

$- 11$

Step 2.3

Convert $- 11$ to decimal.

$y = - 11$

Step 3

Find the point at $x = - 5$ .

Tap for more steps...

Step 3.1

Replace the variable $x$ with $- 5$ in the expression.

$f (- 5) = 4 {((- 5) + 5)}^{3} - 7$

Step 3.2

Simplify the result.

Tap for more steps...

Step 3.2.1

Simplify each term.

Tap for more steps...

Step 3.2.1.1

Add $- 5$ and $5$ .

$f (- 5) = 4 \cdot 0^{3} - 7$

Step 3.2.1.2

Raising $0$ to any positive power yields $0$ .

$f (- 5) = 4 \cdot 0 - 7$

Step 3.2.1.3

Multiply $4$ by $0$ .

$f (- 5) = 0 - 7$

Step 3.2.2

Subtract $7$ from $0$ .

$f (- 5) = - 7$

Step 3.2.3

The final answer is $- 7$ .

$- 7$

Step 3.3

Convert $- 7$ to decimal.

$y = - 7$

Step 4

Find the point at $x = - 4$ .

Tap for more steps...

Step 4.1

Replace the variable $x$ with $- 4$ in the expression.

$f (- 4) = 4 {((- 4) + 5)}^{3} - 7$

Step 4.2

Simplify the result.

Tap for more steps...

Step 4.2.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1

Add $- 4$ and $5$ .

$f (- 4) = 4 \cdot 1^{3} - 7$

Step 4.2.1.2

One to any power is one.

$f (- 4) = 4 \cdot 1 - 7$

Step 4.2.1.3

Multiply $4$ by $1$ .

$f (- 4) = 4 - 7$

Step 4.2.2

Subtract $7$ from $4$ .

$f (- 4) = - 3$

Step 4.2.3

The final answer is $- 3$ .

$- 3$

Step 4.3

Convert $- 3$ to decimal.

$y = - 3$

Step 5

Find the point at $x = - 3$ .

Tap for more steps...

Step 5.1

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

$f (- 3) = 4 {((- 3) + 5)}^{3} - 7$

Step 5.2

Simplify the result.

Tap for more steps...

Step 5.2.1

Simplify each term.

Tap for more steps...

Step 5.2.1.1

Add $- 3$ and $5$ .

$f (- 3) = 4 \cdot 2^{3} - 7$

Step 5.2.1.2

Raise $2$ to the power of $3$ .

$f (- 3) = 4 \cdot 8 - 7$

Step 5.2.1.3

Multiply $4$ by $8$ .

$f (- 3) = 32 - 7$

Step 5.2.2

Subtract $7$ from $32$ .

$f (- 3) = 25$

Step 5.2.3

The final answer is $25$ .

$25$

Step 5.3

Convert $25$ to decimal.

$y = 25$

Step 6

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

$\begin{array}{c} x & y \\ - 7 & - 39 \\ - 6 & - 11 \\ - 5 & - 7 \\ - 4 & - 3 \\ - 3 & 25 \end{array}$

Step 7

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 7 & - 39 \\ - 6 & - 11 \\ - 5 & - 7 \\ - 4 & - 3 \\ - 3 & 25 \end{array}$

Step 8