Question

Move the slider h so that the graph of y = x 2 gets shifted to the right 3 units. Then type the new function, f ( x ) in the answer box h = 0.00 f ( x ) = x 2 Using function notation, i.e. f(x)= , enter the function that results from the transformation.

Answer 1

The function f(x) = x^2 shifted to the right by 3 units is represented as f(x) = (x - 3)^2.

Step-by-step explanation:

To move the graph of the function f(x) = x^2 to the right by 3 units, you need to adjust the input variable x. To achieve this shift, you must subtract 3 from x before it is squared in the function. Therefore, the new function after the graph has been shifted to the right by 3 units will be f(x) = (x - 3)^2. This is because each x value on the graph of y = x^2 will be increased by 3 to reach its new position on the graph of f(x).

Answer 2

Answer: y = (x-3) ^2

Explanation :

GIVEN THE GRAPH

`\text{ y = x}^2`

Shifting this 3 units to the right will result in the new function :

`y\text{ = \lparen x-3\rparen}^2`

Since we are shifting y = x^2 to the right , the sign needs to be negative (-3) . because (x-3) = 0 will result in x = 3 units upwards .

See the image below for the new resulting function :

The graph above shows y = x^2 being moved to the right by 3 units to form a new function y = (x-3)^2 .