Question

Write a formula for the function in the image below. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!negative cubic function with center at (2,1)The new equations f(x)=Answer

Answer 1

Based on the graph shown above, a formula for the function is
`f(x)=-(x-2)^3+1`.

In Mathematics and Euclidean Geometry, a radical function, cubic function or a cube root function can be represented by using the following mathematical equation:

`f(x)=a\sqrt[3]{x-h} +k` or
`f(x)=(x-h)^3+k`

where:

• h represent the horizontal shift.
• k represent the vertical shift.

Based on the graph shown above, we can logically deduce that the parent function was shifted to the right by 2 units and up 1 unit. Therefore, we would determine the value of a by using these values and the x-intercept (3, 0);

`f(x)=a\sqrt[3]{x-h} +k\\\\0=a\sqrt[3]{3-2} +1\\\\0=a+1\\\\a=-1`

In this context, an equation for this cubic function can be written as follows;

`f(x)=a\sqrt[3]{x-h} +k\\\\f(x)=-1 \cdot \sqrt[3]{x-2} +1\\\\f(x)=-(x-2)^3+1`

Answer 2

Given:

Graph is given.

Therefore the equation of the given graph is

`f(x)=(2-x)^3+1`