1. "All real numbers" is the one domain of the equation y = x2 − 6x + 1 among the following choices given in the question. The correct option among all the options that are given in the question is the fourth option or option "D".
2. "Left by 4 units" is the one among the following choices given in the question that gives the direction and by how many units f(x) be shifted to obtain g(x). The correct option is option "A".
The equation is a quadratic equation and we know that the polynomial function is defined for all of the x i.e. for all the real values.
Hence, the domain is:
All real numbers.
Ques 2)
Functions f(x) and g(x) are given by:
and
i.e. the function g(x) could be written as:
We know that the translation of the original function f(x) to f(x+k) is a shift of the function f(x) k units to the right or left depending whether k is negative or positive respectively.
The correct answer is C because the problem showed ( x + 20 ) and ( x + 8 ) two times in the problem. That explains why there is a two outside of the parentheses. Hope I helped! :)
