Question

Function g can be thought of as a translated (shifted) version of f(x) = x2.

Answer 1

Given:

The given parent function is $f(x)=x^2$

We need to determine the equation of the new translated (shifted) function g(x).

Vertical stretch:

The general rule to shift the graph f(x), to shift c units upward is $g(x)=f(x)+c$

From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.

Thus, applying the above rule, we get;

$g(x)=x^2+1$

Horizontal stretch:

The general rule to shift the graph f(x) to shift c units to the left is $g(x)=f(x+c)$

From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.

Thus, applying the above rule, we have;

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

Equation of the new function g(x):

From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.

Thus, we have;

$g(x)=(x+2)^2+1$

Therefore, the equation of the new function g(x) is $g(x)=(x+2)^2+1$