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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Answer:
Step-by-step explanation:
We have the function:
And we want to write its equation after being: 1) Flipped over the x-axis, 2) shifted 4 units down, and 3) shifted 1 unit to the left.
To denote a flip over the x-axis, we multiply the function by -1. Hence:
Is our function flipped over the x-axis.
To shift n units vertically, we simply add n to our function.
Since we are going 4 units downwards, we will add -4 to our function. Hence:
Finally, to shift n units horizontally, we substitute our variable for .
Since we are shifting 1 unit to the left, n=-1. Hence, we will substitute for . Therefore:
So, our final function is:
Express your answer in lowest terms.
in.
Answer:
Step-by-step explanation:
Given: In the last 2 weeks, a plant grew and respectively.
To find the total plant growth in the last 2 weeks, we need to add the growth registered in each week.
Thus, the total growth =
Hence, the plant grow in the last 2 weeks.