Domain and Range — Quiz

Question 3 • Mathematics III

What are the domain and range of the function f of x is equal to 3 fourths x plus 5 ?

Answer

domain: open paren negative infinity comma infinity close paren range: open paren negative infinity comma infinity close paren

domain: open paren 3 fourths comma infinity close paren range: open paren 5 comma infinity close paren

domain: open paren negative infinity comma 3 fourths close paren range: open paren 5 comma infinity close paren

domain: open paren 3 fourths comma infinity close paren range: open paren negative infinity comma 5 close paren

Explanation

The function is f(x) = (3/4)x + 5, a linear function with no restrictions on x, so its domain is all real numbers. Since the slope 3/4 is nonzero, the function can also produce every real output as x varies over all real numbers. Therefore, both the domain and range are (−∞, ∞), matching choice B.

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