Question

1.) Identify the domain of the equation y = x2 − 6x + 1.

A.) x ≤ 3
B.) x ≥ −8
C.) x ≥ −2
D.) All real numbers

2.) Functions f(x) and g(x) are shown below:

f(x) = x^2
g(x) = x^2 + 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?

A.) Left by 4 units
B.) Right by 4 units
C.) Left by 8 units
D.) Right by 8 units

Answer 1

1)

The domain is

D.) All real numbers

2)

The correct answer is:

A.) Left by 4 units

Explanation:

Ques 1)

The equation of a parabola is:

`y=x^2-6x+1`

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:

`f(x)=x^2`

and
`g(x)=x^2+8x+16\\\\i.e.\\\\\\g(x)=(x+4)^2`

i.e. the function g(x) could be written as:

`g(x)=f(x+4)`

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.

Here k=4>0

Hence, the shift is 4 units to the left.

Answer 2

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".