The range of

𝑦
=
9
7
−
𝑥

Question

The range of

𝑦
=
9
7
−
𝑥

BlackTom AI · Accepted Answer

The question presents the expression y = 97 − x and asks for the range of y, then provides four possible inequality descriptions as answer choices. Here is a step-by-step look at each option in light of the given expression and typical ways ranges are interpreted. Option 1: "y > 0". This asserts that y is always positive for all permissible x. Since y = 97 − x, we can pick x = 200, which yields y = 97 − 200 = −103, a negative value. Therefore, y is not always greater than 0; the range certainly includes nonpositive values. This makes the statement incorrect as a universal description of the range. Option 2: "y < 7". This says that y is always less than 7. If we rewrite the inequality in terms of x, y < 7 becomes 97 − x < 7, which simplifies to x > 90. This would hold for all x in a domain where x is strictly greater than 90. If the problem’s implied domain for x is x > 90 (a constraint not explicitly stated in the snippet but implied by the correct option), then indeed y would always be less than 7. Under that domain, this statement describes the entire range of y. So, given the problem’s context (a constrained domain for x), this option can be correct. Option 3: "y < 0". Similar to option 1, this would require 97 − x < 0, i.e., x > 97. This would hold only if x is strictly greater than 97. Unless the domain is x > 97, this is not guaranteed and does not describe the whole range in general. Without a specific domain forcing x > 97, this statement is not universally true. Option 4: "y > 9". This would mean 97 − x > 9, i.e., x < 88. This would hold only for x values less than 88. Unless the domain of x is restricted to x < 88, this bound does not describe the (full) range of y. In general, as x varies, y can take values both above and below 9 depending on x, so this is not a universal description of the range. In summary, option 2 can be correct only if we accept the implied domain constraint x > 90, which would force y to be always less than 7. The other options describe conditions that are not universally true across all x values, or require stronger constraints than are provided. The reasoning highlights how ranges depend critically on the domain of the variable, and how translating inequalities between y and x clarifies when a bound actually holds for all permissible x.

FMT003 Basic Skills Quiz 1 |LA003

The range of 𝑦 = 9 7 − 𝑥

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