What is the range of #f(x) = 3x + 4#?

1 Answer

#f(x)=3x+4# is a linear function, and so the domain and range for that functions is all real numbers. In fact, the domain and range for any linear function is all real numbers.

So, in interval notation:

The domain (or possible input(#x#)-values) is: (-∞,∞)

The range (or possible output(#y#)-values) is: (-∞,∞)

*Note the round brackets ( ) used.Since infinity isn't a number, the function isn't exactly "defined" there, it just keeps tending to infinity. If the function was defined on a certain interval, we would put [square brackets] around it

When you're trying to figure out a domain, you can think about if the function is continuous. Is there any place where the function is not defined, so you're not allowed to plug into a value (like a 0 in the denominator)? Are there any places where there are asymptotes?

In the case of linear functions like #f(x)=3x+4# , you can plug in all sorts of negative and positive #x# and #y# and get a solution (infinitely many actually, which is why the domain and range are continuous from negative infinity to positive infinity). Graphically, this just means that the graph is a line that keeps getting larger and larger as #x# gets infinitely large, and smaller and smaller as #x# gets infinitely small.

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