This question is a little dubious, because letters C and D are incorrect. The absolute value function is defined like this: |x| = x for a positivex, |x| = −x for a negativex (in which case −x is positive), and |0| = 0.
Alternative C is incorrect because the absolute value of x is not - x when x is 0, it should be x when x=0.
However, alternative D is incorrect because it doesn't account 0 at all, which is a value completely defined in the domain of the function f(x)= |x|.
I would say alternative D.
5 years ago
Answered By Sophia E
I honestly feel unsure about the answer, especially because of the way answers B and C are worded. If you're a visual learner, you may want to consider the graph of $f\left(x\right)=\left|x\right|$ƒ(x)=|x|.
A would be the correct definition since $\left|x\right|=x$|x|=x for $x>0$x>0 , $\left|x\right|=-x$|x|=−x for $x<0$x<0 and $\left|0\right|=0$|0|=0 .
B and C both made me think (at least) a little longer (possibly because I'm overthinking the conditions given in the answers). I get that when you plug in 0 for any positive x, then it satisfies the condition $x\ge0$x≥0. Similarly, when you plug in $-x=0$−x=0, then the answer is still 0, so then that would satisfy the condition $x\le0$x≤0. Since 0 satisfies both conditions in B and C, then B and C are correct definitions.
D says that "$\left|x\right|=x$|x|=x for $x>0$x>0 [and] $\left|x\right|=-x$|x|=−x for $x<0$x<0." This implies that 0 is not included in the function |x|, which would therefore create a totally different function.
To answer the original question of what an incorrect definition is for an absolute value, based on my thought process, I would say D is the incorrect definition.
5 years ago
Answered By Leonardo F
This question is a little dubious, because letters C and D are incorrect. The absolute value function is defined like this: |x| = x for a positive x, |x| = −x for a negative x (in which case −x is positive), and |0| = 0.
Alternative C is incorrect because the absolute value of x is not - x when x is 0, it should be x when x=0.
However, alternative D is incorrect because it doesn't account 0 at all, which is a value completely defined in the domain of the function f(x)= |x|.
I would say alternative D.
5 years ago
Answered By Sophia E
I honestly feel unsure about the answer, especially because of the way answers B and C are worded. If you're a visual learner, you may want to consider the graph of $f\left(x\right)=\left|x\right|$ƒ (x)=|x|.
A would be the correct definition since $\left|x\right|=x$|x|=x for $x>0$x>0 , $\left|x\right|=-x$|x|=−x for $x<0$x<0 and $\left|0\right|=0$|0|=0 .
B and C both made me think (at least) a little longer (possibly because I'm overthinking the conditions given in the answers). I get that when you plug in 0 for any positive x, then it satisfies the condition $x\ge0$x≥0. Similarly, when you plug in $-x=0$−x=0, then the answer is still 0, so then that would satisfy the condition $x\le0$x≤0. Since 0 satisfies both conditions in B and C, then B and C are correct definitions.
D says that "$\left|x\right|=x$|x|=x for $x>0$x>0 [and] $\left|x\right|=-x$|x|=−x for $x<0$x<0." This implies that 0 is not included in the function |x|, which would therefore create a totally different function.
To answer the original question of what an incorrect definition is for an absolute value, based on my thought process, I would say D is the incorrect definition.
Hope this helps!
Attached Graph: