Y is less than or equal to 5.
The range of the absolute value function f(x) = 5 - |x - 4| is (-∞ , 5] because the function will always be less than or equal to 5, but there's no lower limit as the function will decrease indefinitely as |x - 4| increases.
The function given is f(x) = 5 - |x - 4|, which represents an absolute value function. The range of a function refers to the possible values of f(x) or y in the function. In general, the absolute value function has a range of all non-negative numbers. However, because the function is subtracted from 5, the values of this particular function will decrease as x moves away from 4, in either direction.
Therefore, the maximum value of the function occurs when the absolute value equals to zero (i.e., x = 4), then f(x) = 5 - 0 = 5. As you move away from 4, the absolute value increases and thus subtracts more from 5, making f(x) smaller. So, f(x) will always be less than or equal to 5, but there is no lower limit, as the function will continue to decrease indefinitely as |x - 4| increases. Hence the range of the function f(x) = 5 - |x - 4| is (-∞ , 5].
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10-
(1,8)
(0,4)
A. f(x) = 4 . (2)
B. f(x) = 8. (4)*
C. f(x) = 4. (8)*
D. f(x) = 2 · (4)
Answer: A. f(x) = 4 . (2)
Step-by-step explanation: Disregard answer above. I took the quiz and it was wrong.
The answer should be 55 degrees.
The quadratic expression (x+4)² = x² + 8x + 16.
The given expression is,
(x+4)²
The expression (x+4)² represents a mathematical operation called "squaring."
To expand it, we need to multiply the expression by itself.
So, (x+4)² becomes (x+4) * (x+4).
When we multiply these terms, we apply the distributive property and combine like terms.
After simplifying, we get x² + 8x + 16.
Or we can directly use the identity,
(a+b)² = a² + b² + 2ab
Here a = x and b = 4
(x+4)² = x² + 4² + 8x
Hence,
(x+4)² = x² + 8x + 16
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