y=x+2−−−−−√3 is a(n) function.

Question

GPT-4o mini · Answer

To determine if $ y = \sqrt{x + 2} - 3 $ is a function, we need to understand the definition of a function. A function assigns exactly one output (value of $ y $) for each input (value of $ x $). ### Analysis: 1. **Domain**: The expression $ \sqrt{x + 2} $ is defined for $ x + 2 \geq 0 $ (since you cannot take the square root of a negative number). This implies: $$ x + 2 \geq 0 \implies x \geq -2 $$ Thus, the domain of the function is $ x \in [-2, \infty) $. 2. **Output for each input**: For each value of $ x $ in the domain, there is a unique value of $ y $: $$ y = \sqrt{x + 2} - 3 $$ Since the square root function produces exactly one output for each non-negative input, and by subtracting 3, we do not change that uniqueness. ### Conclusion: Yes, $ y = \sqrt{x + 2} - 3 $ is a function, since for each $ x $ in its domain, there is a unique $ y $.

local.trin · Answer

is it an square root ,linear, cube root, cubic

GPT-4o mini · Answer

The expression $ y = \sqrt{x + 2} - 3 $ is classified as a **square root function**. ### Explanation of Classifications: 1. **Square Root Function**: This type of function is generally of the form $ y = \sqrt{f(x)} $ where $ f(x) $ is some expression. In your case, it is $ y = \sqrt{x + 2} - 3 $, which is a square root function shifted down by 3 units. 2. **Linear Function**: A linear function is of the form $ y = mx + b $ where $ m $ and $ b $ are constants. The given function does not conform to this form due to the presence of the square root. 3. **Cube Root Function**: A cube root function is generally of the form $ y = \sqrt[3]{f(x)} $. The given function is not a cube root. 4. **Cubic Function**: A cubic function is generally of the form $ y = ax^3 + bx^2 + cx + d $. The given function does not fit this form either. ### Summary: The function $ y = \sqrt{x + 2} - 3 $ is specifically a **square root function** due to the square root operation involved with its expression.

local.trin · Answer

y=x3+3 is a(n) function.

GPT-4o mini · Answer

Yes, $ y = x^3 + 3 $ is a function. ### Explanation: 1. **Definition of a Function**: A function assigns exactly one output value (in this case, $ y $) for each input value (in this case, $ x $). 2. **Expression Analysis**: The given expression $ y = x^3 + 3 $: - For every real number input $ x $, the output $ y $ is obtained by cubing $ x $ and then adding 3. - The cube function $ x^3 $ is defined for all real numbers, and it produces a unique output for each input. 3. **Graph**: The graph of $ y = x^3 + 3 $ is a standard cubic curve shifted up by 3 units. It is continuous and does not have any breaks, loops, or restrictions in its domain. ### Conclusion: Based on the above considerations, $ y = x^3 + 3 $ is indeed a function. Specifically, it is a **cubic function** due to the $ x^3 $ term.

local.trin · Answer

is it an square root ,linear, cube root, cubic

GPT-4o mini · Answer

The expression $ y = x^3 + 3 $ is classified as a **cubic function**. ### Explanation of Classifications: 1. **Square Root Function**: A square root function is generally in the form $ y = \sqrt{f(x)} $, where $ f(x) $ is some expression. The given function does not fit this form. 2. **Linear Function**: A linear function takes the form $ y = mx + b $, where $ m $ and $ b $ are constants. The given function $ y = x^3 + 3 $ is not linear due to the $ x^3 $ term. 3. **Cube Root Function**: A cube root function is generally in the form $ y = \sqrt[3]{f(x)} $. The given function is not a cube root function since it is defined as $ y = x^3 + 3 $. 4. **Cubic Function**: A cubic function is generally in the form $ y = ax^3 + bx^2 + cx + d $. The provided function $ y = x^3 + 3 $ fits this form, where $ a = 1 $, $ b = 0 $, $ c = 0 $, and $ d = 3 $. ### Summary: Thus, the function $ y = x^3 + 3 $ is specifically a **cubic function**.

local.trin · Answer

y=x+2 is a(n) function

GPT-4o mini · Answer

Yes, $ y = x + 2 $ is a function. ### Explanation: 1. **Definition of a Function**: A function assigns exactly one output (value of $ y $) for each input (value of $ x $). The equation $ y = x + 2 $ meets this definition because for every value of $ x $, there is exactly one corresponding value of $ y $. 2. **Type of Function**: The given equation is a **linear function**. Linear functions have the general form $ y = mx + b $, where: - $ m $ is the slope (here, $ m = 1 $), - $ b $ is the y-intercept (here, $ b = 2 $). This means that the graph of this function is a straight line with a slope of 1, intersecting the y-axis at the point $ (0, 2) $. ### Conclusion: In summary, $ y = x + 2 $ is a **linear function**.