Can someone help me please? the last point of the first graph ends on 6
1 answer:
Answer:
a) Yes
b) for reference, draw the line y = x, and reflect it over that, this reflection will be your inverse. Or switch the x and y values of each point of the function.
Here is a photo of the original function in black, it's inverse in red, and the line of reflection y = x in blue:
c) No, because it fails the vertical line test, when you draw a vertical line across the inverse function, it hits it more than once.
d) Domain of the original function: -6 ≤ x ≤ 6 ; x(the domain) is greater than or equal to -6 and less than or equal to 6.
e) Domain of inverse function: 0 ≤ x ≤ 4 ; x(the domain) is greater than or equal to 0 and less than or equal to 4.
f) Range of the original function: 0 ≤ y ≤ 4 ; y(the range) is greater than or equal to 0 and less than or equal to 4.
e2) Range of the inverse function: -6 ≤ y ≤ 6 ; y(the range) is greater than or equal to -6 and less than or equal to 6.
f2) x-intercept of original function: -6
g) y-intercept of the inverse function: -6
h) x-intercept of the inverse function: 4
i) y-intercept of the original function: 4
j) (2,2) or any point where the x, and y are the same within the function, or the point where the function intersects y = x.
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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) ⇒ ∞
