Can the graph of a function be a horizontal line? Explain your reasoning.
1 answer:
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Answer:
The answers are:
a) is FALSE.
b) is TRUE.
c) is FALSE.
d) is FALSE.
e) is FALSE.
f) is TRUE.
g) is FALSE.
h) is FALSE.
Step-by-step explanation:
We can show that the FALSE statement are, in fact, false finding an example where the equality fails.
a) Take x=2 and y=3 and notice that (2+3)² = 25, while 2²+3²=4+9=13.
b) (x+y)² = (x+y)(x+y)=x²+xy+xy+y² = x² +2xy +y².
c) Take x=2 and y=3 and notice that 2/(2+3) = 2/5 which is different from 1/3.
d) Take x=2 and y=3 and notice that 2-(2+3) = 2-5=-3 which is different from 3. Recall that x-(x+y) = x-x-y=-y.
e) Take x=-2, and notice that [tax]\sqrt{(-2)^2} = \sqrt{4} = 2[/tex] which is different from -2.
f) The previous example illustrate why this is true.
g) Take x=1, and notice that which is different from 3.
h) Take x=2 and y=3 and notice that 1/(2+3)=1/5 and 1/3+1/2 = 5/6.