How would you graph the solution set of x - 6 < -3?
1 answer:
Answer:
Draw an open circle on 3 and shade to the left.
Step-by-step explanation:
Given:
The inequality given is:
In order to solve for 'x', we add 6 on both sides of the inequality. This gives,
Therefore, the solution is 'x' less than 3.
So, 'x' includes all the values that are less than 3 and excluding 3 as the inequality sign is less than.
So, on a number line, the values that are less than 3 are to the left of 3. So, we shade to the left. Also, 3 is excluded from the solution. So, we use an open circle as shown below.
So, the first option is the correct option.
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We must recall that a horizontal asymptote is the value/s of y that the given function approaches to but never reaches. To find this in a rational function, we compare the expressions with highest degree in the numerator and denominator. There are three possible outcome when this happens.
1. if the highest degree (highest exponent) in the numerator is bigger than that of the denominator, then there won't be any horizontal asymptote.
2. if the highest degree in the denominator is bigger, then the horizontal symptote would be y = 0.
3. if they have the same highest degree, then we just get the quotient of their coefficient.
Now, going back to our function, we have
From this we can see that the highest degree in the numerator is 1 (from 2x) and 2 (from x²) for the denominator. Clearly, it shows that its denominator has a higher degree. And from our discussion, we can conclude that the horizontal asymptote would be y = 0.
Answer: y = 0
1. if the highest degree (highest exponent) in the numerator is bigger than that of the denominator, then there won't be any horizontal asymptote.
2. if the highest degree in the denominator is bigger, then the horizontal symptote would be y = 0.
3. if they have the same highest degree, then we just get the quotient of their coefficient.
Now, going back to our function, we have
From this we can see that the highest degree in the numerator is 1 (from 2x) and 2 (from x²) for the denominator. Clearly, it shows that its denominator has a higher degree. And from our discussion, we can conclude that the horizontal asymptote would be y = 0.
Answer: y = 0