Find the equation in slope- intercept from that describes a line through (4,-2) slope-3
1 answer:
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Answer:
b) There is translation 3 units to the right and 1 unit up
c) The domain is {x I x > 3}
The equation of the asymptote is x = 3
Step-by-step explanation:
* Lets revise the rule of the translation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
b) ∵ f(x) =
∵ The parent function is
∴ x is changed to (x - 3), that means there is a translation 3 units
to the right
∵ We add the parent function by 1, that means there is a translation
1 unit up
* There is translation 3 units to the right and 1 unit up
c) To find the domain of the function, find the values of x which
make the function undefined
∵ is undefined
∴ x - 3 can not be 0
∵ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∴ The domain of the function is all real number greater than 3
* The domain is {x I x > 3}
∵ x can not be 3
∴ There is a vertical asymptote, its equation is x = 3
* The equation of the asymptote is x = 3
# Look to the attached graph for more understand for the domain
and the equation of the asymptote
If it has a single zero that means it has to be just touching the x-axis with its tip.
We know that if it has only one zero, the discriminant equals 0.
So,
Solving for k,
.
Hope this helps.