The domain of
𝑦
=
5
𝑥
−
15

Question

The domain of 
𝑦
=
5
𝑥
−
15

BlackTom AI · Accepted Answer

To determine the domain, we examine where the expression for y is defined.
Option 1: x ≥ 3. This would impose a restriction on x, but for the function y = 5x − 15 there is no division by x or any operation that would fail for x values; thus this is unnecessarily restrictive and incorrect.
Option 2: x < 3. Similar to option 1, this imposes a cut in the domain that does not exist for a simple linear function. The line 5x − 15 is defined for every real x, so limiting to x < 3 is incorrect.
Option 3: x > 3. Again, this excludes many valid x values and is not required by the expression. The function does not have a domain that starts only after 3; it accepts all real numbers, so this option is incorrect.
Option 4: x ≤ 3. This choice also imposes an artificial boundary that does not pertain to the expression 5x − 15. There is no restriction to x being less than or equal to 3, so this is incorrect.
If the expression were 5/x − 15, we would instead have x ≠ 0 as the domain, but the provided correct answer indicates the expression is interpreted as 5x − 15, which is defined for all real x. Therefore, the appropriate domain is all real numbers, matching the given correct option.

FMT003 Basic Skills Quiz 1 |LA003

The domain of 𝑦 = 5 𝑥 − 15

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