Question

Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units right and 4 units up on the parent function f(x)=x^2

Answer 1

Answer:

i) The rule of the translation is (x. y) ------> (x +2, y -4)

ii) Attache the graph.

Step-by-step explanation:

Given: f(x) = x^2

The rule of the translation function is 2 units right and 4 units down.

Let's g(X) is the new function.

(x, y ) ---> (x + 2, y - 4)

The translation function g(x) = (x - 2)^2 - 4

Answers:

i) The rule of the translation is (x. y) ------> (x +2, y -4)

ii) Attache the graph of the function g(x) = (x -2)^2 - 4

Answer 2

Answer:

$g(x) = (x+3)^2+4$

Step-by-step explanation:

The function when a function f(x) is translated a unit right,

g(x) = f(x + a),

Translated a unit left,

g(x) = f(x - a)

Translated a unit upward,

g(x) = f(x) + a

Translated a unit downward,

g(x) = f(x) + a

Given,

The parent function is,

$f(x)=x^2$

Hence, the function performing the translation 3 units right then translating 4 unit up,

$g(x) = (x+3)^2+4$,