How do you find the range of f(x) = 3x + 4?
Expert Answers
| Certified Educator
calendarEducator since 2013
write5 answers
starTop subject is Math
The range of the function is all possible values of y.
Since f(x) = 3x + 4 is a linear function, the range would be all real numbers.
All Real Numbers, or ` (-oo,+oo) `
Related Questions
- Find the domain and range of the function `f(x) = |x-4|/(x-4)`
- 1 Educator Answer
- `f(-1)` Find the value if f(x) = 3x - 4
- 1 Educator Answer
- Find the domain f=(5x+4) / (x^2+3x+2)
- 1 Educator Answer
- Find the inverse of the function f(x) = e^(3x - 5).
- 2 Educator Answers
- use a chain rule to find the derivative of f(x)=e^3x
- 2 Educator Answers
| Certified Educator
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You should evaluate the limits of the function to `+-oo` , such that:
`lim_(x->-oo)(3x + 4) = 3*lim_(x->-oo)(x) + 4 = 3*(-oo) + 4 = -oo`
`lim_(x->oo)(3x + 4) = 3*lim_(x->oo)(x) + 4 = 3*(oo) + 4 = oo`
Since the function is continuous, hence, the range of the function is `(-oo,+oo).`
You also may notice that the graph of the function `f(x) = 3x + 4` , that is the line, is continuous and it goes up at x increases from `-oo ` to `+oo.`
Hence, evaluating the range of the function yields `f(x) = y in (-oo,+oo).`