Answer:
(-∞, ∞)
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values).
An asymptote is a line that the curve gets infinitely close to, but never touches.
The arrows on either end of a graphed curve show that the function <u>continues indefinitely</u>. Therefore, we cannot assume there is an asymptote at x = -3 as we cannot see what happens to the curve as x approaches -∞.
Therefore, the domain of the given function is unrestricted:
- Solution: { x | -∞ < x < ∞ }
- Interval notation: (-∞, ∞)
Insert x + 3 instead of x into the equation of the function f(x):
f(x) = 3 - 6x²
f(x + 3) = 3 - 6(x + 3)²
use (a + b)² = a² + 2ab + b²
= 3 - 6(x² + 2(x)(3) + 3²) = 3 - 6(x² + 6x + 9)
use distributive property
= 3 + (-6)(x²) + (-6)(6x) + (-6)(9) = 3 - 6x² - 36x - 54
combine like terms
= -6x² - 36x - 51
<h3>Answer: f(x + 3) = -6x² - 36x - 51</h3>
Answer:
23
Step-by-step explanation:
Remember PEMDAS/order of operations (Parentheses, exponent, multiplication, division, addition, subtraction)
10*1/2+(-6)(-3)
10*1/2+18
5+18
23
