Respuesta :
Answer:
B) As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
Step-by-step explanation:
By looking at the given graph, we can infer
As x --> -∞, the y-values tends to -∞
Similarly, as x approaches negative infinity, f(x) approaches negative infinity
Y is value is nothing but the function of x. That is f(x).
Therefore, the answer is
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity
Hope this helped
The statement that describes the end behavior of the function f(x) = 3|x − 7| − 7 is B. As x approaches negative infinity, f(x) approaches positive infinity
B. As x approaches negative infinity, f(x) approaches positive infinity is the correction option.
To determine the statement that describes the end behavior of the function f(x) = 3|x − 7| − 7, we will examine each of the options and determine which is correct.
For A. As x approaches negative infinity, f(x) approaches negative infinity.
Infinity in mathematics means something that is unlimited, endless, without bound.
The sign | | is called modulus which gives the absolute value of the number it encloses without regard to the sign.
Now, if x approaches negative infinity,
that is, on a number line, x approaches the numbers on the negative side, say x approaches -3 to -4 to -5, to ..., -101 to -102 to ... -3000 to -3001 to ... and so on.
Testing for two out of these values, we will determine the end behavior of the function f(x)
From the question,
f(x) = 3|x − 7| − 7
when x = -101
then, f(x) = 3|-101 − 7| − 7
f(x) = 3|-108| − 7
f(x) = 3 × 108 − 7
f(x) = 324 -7
f(x) = 317
Also, when x = -3000
then, f(x) = 3|-3000− 7| − 7
f(x) = 3|-3007| − 7
f(x) = 3 × 3007 − 7
f(x) = 9021 - 7
f(x) = 9014
Here, we observe that as x approaches negative infinity, f(x) does not approach negative infinity but approaches positive infinity
∴ A is not correct
For B. As x approaches negative infinity, f(x) approaches positive infinity.
As shown above, we observe that as x approaches negative infinity, f(x) approaches positive infinity.
∴ B is correct
For C. As x approaches positive infinity, f(x) approaches negative infinity
Now, if x approaches positive infinity,
that is, on a number line, x approaches the numbers on the positive side, say x approaches 3 to 4 to 5, to ..., 101 to 102 to ... 3000 to 3001 to ... and so on
Testing for two out of these values, we will determine the end behavior of the function f(x)
f(x) = 3|x − 7| − 7
when x = 102
f(x) = 3|102 − 7| − 7
f(x) = 3|95| − 7
f(x) = 3 × 95 − 7
f(x) = 285 − 7
f(x) = 278
Also, when x = 3000
f(x) = 3|3000 − 7| − 7
f(x) = 3|2993| − 7
f(x) = 3 × 2993 − 7
f(x) = 8979 − 7
f(x) = 8972
Here, we observe that as x approaches positive infinity, f(x) does not approach negative infinity but approaches positive infinity
∴ C is not correct
For D. As x approaches positive infinity, f(x) is no longer continuous.
As shown above for C, we can observe that f(x) is continuous.
∴ D is not correct
Hence, the statement that describes the end behavior of the function f(x) = 3|x − 7| − 7 is B. As x approaches negative infinity, f(x) approaches positive infinity
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