I need help on this question ):
1 answer:
You might be interested in
Let's rewrite the equation as
This should be enough to convince you that the equation has no solutions, no matter which value for k you choose. In fact, the left hand side of the equation is an absolute value, which by definition is always positive, or zero in the worst case.
The equality asks for this quantity to equal -3, a negative number.
A non-negative quantity can never equal a stricktly negative quantity, so the equation has no solutions.
Answer:
The translation did not effect the domain
The translation effected the range
Step-by-step explanation:
The given graph represents f(x) = IxI
The domain of f(x) is {x : x ∈ R}, where R is the set of real numbers
The range of f(x) is {y : y ≥ 0}
The graph of g(x) is attached down
g(x) = IxI + 4
The domain of g(x) is {x : x ∈ R}, where R is the set of real numbers
The range of g(x) is {y : y ≥ 4}
The graph of g(x) is the image of the graph of f(x) after translate it 4 units up
∵ The translation is vertically
∴ The domain of f(x) = the domain of g(x)
∵ The domain of f(x) is {x : x ∈ R}
∴ The domain of g(x) is {x : x ∈ R}
∴ The translation did not effect the domain
∵ g(x) = f(x) + 4
∵ The range of f(x) is {y : y ≥ 0}
- Add 4 to the value 0
∴ The range of g(x) is {y : y ≥ 0 + 4}
∴ The range of g(x) is {y : y ≥ 4}
∴ The range of g(x) not equal the range of f(x)
∴ The translation effected the range
