Simplify the expression |ab| if a<0 and b>0
1 answer:
Answer:
Step-by-step explanation:
Given:
The expressions to simplify are:
1.
We know that, product of a negative number and a positive number is always negative.
Here, 'a' is less than 0 or a negative number. 'b' is greater than 0 or a positive number. The product of 'a' and 'b' is a number less than 0 or a negative number. Now, we need to find the absolute value of their product. The absolute value is never negative. So, in order to make the product positive, we multiply the product by -1 as product of two negative numbers is always positive.
Therefore,
2.
Here, also, 'b' is less than 0 or a negative number. Therefore, the number '2b' is a negative number So, in order to write this without the absolute value sign, we have to multiply '2b' by -1 to make the product always positive.
Therefore,
3.
This is also similar to the one above. Since 'c' is a negative number, we need to multiply it by -1 when we remove the absolute value sign.
Thus,
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The domain is all real values except the ones that will make the denominator zero.
The domain is all real values except, x=2.5.
ii) To find the vertical asymptote, we equate the denominator to zero and solve for x.
iii) If we equate the numerator to zero, we get;
This implies that;
iv) To find the y-intercept, we put x=0 into the given function to get;
.
.
.
v)
The degrees of both numerator and the denominator are the same.
The ratio of the coefficient of the degree of the numerator to that of the denominator will give us the asymptote.
The horizontal asymptote is .
vi) The function has no common factors that are at least linear.
The function has no holes in it.
vii) This rational function has no oblique asymptotes because it is a proper rational function.
