I need help with this asappp
2 answers:
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Answer:
The domain of h(x) is {x : x ∈ R}
The range of the function is {y : y > -9}
The horizontal asymptote is at y = -9
Step-by-step explanation:
* Lets read the problem and solve it
- The exponential function is f(x) = a(b)^x, where a and b are constant
and b is the base , x is the exponent , a is the initial value of f(x)
- The domain of the function is all the values of x which make the
function defined
- The range of the function is the set of values of y that corresponding
with the domain x
- Asymptote on the graph a line which is approached by a curve but
never reached
- A function of the form f(x) = a(b^x) + c always has a horizontal
asymptote at y = c
* Lets solve the problem
∵ h(x) = (0.5)^x - 9
∵ All the values of x make h(x) defined
∵ The domain of the function is the values of x
∴ The domain of h(x) is {x : x ∈ R} ⇒ R is the set of real number
∵ The range of the function is the set of values of y which
corresponding to x
∵ (0.5)^x must be positive because there is no values of x make it
negative value
∴ y must be greater than -9
∴ The range of the function is {y : y > -9}
∵ A function of the form f(x) = a (bx) + c always has a horizontal
asymptote at y = c
∵ h(x) = (0.5)^x - 9
∴ c = -9
∴ The horizontal asymptote is at y = -9
* Look to the attached file for more understanding
Answer:
5 minutes to run 1 kilometer
Step-by-step explanation:
Alonzo takes 12 minutes to run 6 times around a 400-meter track.
6 times around a 400 m track
400 * 6 = 2400 meters
It take 12 minutes to run 2400 meters
2400 meters = 2400/1000 = 2.4km
distance = 2.4 km and time = 12 minutes
Now we find our constant speed
2.4 = speed * 12
divide by 12 on both sides
speed = 0.2
so speed is 0.2 km per minute
Now we find out time when distance = 1km
Distance = speed * time
1 = 0.2 * t
divide by 0.2 on both sides
5 = t
So it take 5 minutes to run 1 kilometer