Answer:
Domain: (-∞, ∞) or All Real Numbers
Range: (0, ∞)
Asymptote: y = 0
As x ⇒ -∞, f(x) ⇒ 0
As x ⇒ ∞, f(x) ⇒ ∞
Step-by-step explanation:
The domain is talking about the x values, so where is x defined on this graph? That would be from -∞ to ∞, since the graph goes infinitely in both directions.
The range is from 0 to ∞. This where all values of y are defined.
An asymptote is where the graph cannot cross a certain point/invisible line. A y = 0, this is the case because it is infinitely approaching zero, without actually crossing. At first, I thought that x = 2 would also be an asymptote, but it is not, since it is at more of an angle, and if you graphed it further, you could see that it passes through 2.
The last two questions are somewhat easy. It is basically combining the domain and range. However, I like to label the graph the picture attached to help even more.
As x ⇒ -∞, f(x) ⇒ 0
As x ⇒ ∞, f(x) ⇒ ∞
Answer:
x = 35
Step-by-step explanation:
Distribute
5x+100 = 7x + 30
combine like terms
100 = 2x + 30
70 = 2x
x = 35
Answer:
12. ∠2 ≅ ∠3
The parallel Lines for these angles are q and p.
The theorem that justifies this is Corresponding Angles, because both are in the same position (the upper right-hand corner) in their group of 4 angles. These angles are also Congruent, because the transversal intersects two parallel lines and two corresponding angles are congruent. Q and P would be the parallel lines and R would be the transversal.
13. ∠6 ≅ ∠7
The parallel lines for these angles would be Q and P.
The theorem that justifies this is Alternate Interior Angles, because this pair of angles are on opposite sides of the Transversal line and on the inside of the parallel lines. This also makes them Congruent angles, because the transversal intersects two parallel lines and two Alternate Interior Angles are Congruent. The two parallel lines are Q and P are parallel because line S intersect them, making line S the Transversal.
14. ∠1 ≅ ∠4
The parallel lines for these angles are R and S.
The theorem that justifies this is Alternate Exterior Angles, because angles 1 and 4 are on opposite sides of the transversal as well as the outside of the parallel lines. This also makes these two angles Vertical Angles, because when a transversal intersects two parallel lines, and the angles are across from each other on opposite sides of the transversal, they are vertical angles. Vertical Angles are always Congruent. So R and S are the parallel lines and line Q is the Transversal because it intersects R and S.
15. m∠5 + m∠8 = 180°
The parallel lines for angles 5 and 8 are R and S.
The theorem that justifies this is Same-Side Interior Angles, because they are on the same side of the Transversal and on the inside of the parallel lines. This also makes angles 5 and 8 Supplementary, because a transversal intersects two parallel lines and Same-side Interior Angles are Supplementary. The parallel lines are R and S because Transversal line P intersects them.
Step-by-step explanation:
Explanations are within the answers for each question above.
Hope this helps!! :)
Answer:
don't have enough imformation
Step-by-step explanation: