91Ó°ÊÓ

Given function :f(x) = 3(x + 1)³ - 2

We want to graph function using transformation.

We will draw of the functionf(x) = 3(x + 1)³ - 2 using transformation as follows:

$$\begin{gathered} f_1\left(x\right)=x^3→f_2\left(x\right)={(x+1)}^3---\left(1\right) \\ {f}_2\left(x\right)={(x+1)}^3→f_3\left(x\right)=3{(x+1)}^3---\left(2\right) \\ {f}_2\left(x\right)=3{(x+1)}^3→f_2\left(x\right)=3{(x+1)}^3-2---\left(3\right) \end{gathered}$$

We will draw step by step the functions f₁, f₂ , f₃ and finally f:

Explanation:

• (1) We obtain the functionf₂ = (x + 1)³ by moving the graph of the function f₁ (x³) by 1 to the left (since the zero point of x + 1 is equal to - 1)
• (2)We obtain the functionf₃ = 3 (x + 1)³ by increasing the y-coordinate of the points from the graph f₂ (x) by 1 to the left
• (3) We get the function f (x) by moving the graph of function f₃ down by 2 (due to - 2 in the 3 (x + 1)³ - 2 )

Let's draw a function using a table:

Graph is given by:

We obtain the graph of the function f₂ by moving the graph f₁ by 1 to the left (i.e. we move the points on the graph by 1 to the left).

We will use the points we calculate in step 3:

Graph is given by:

The graph off₃ will be obtained by increasing the y-coordinates of the points on the graph f₂ 3 times.

We will use the points we calculate in Step 4:

The graph is given by:

We obtain the graph of the function f by moving the graph of the function f along the y-axis by 2 downwards (we will subtract 2 from the points on the graph f₃).

We will use the points we calculated in Step 5:

The graph is given by: