Question

this appears to be a polynomial of degree 1. yes no this function appears to have a positive leading coefficient. yes no this function appears to be g(x). yes no this appears to be a polynomial of degree 1. yes no this function appears to have a positive leading coefficient. yes no this function appears to be g(x). yes no this appears to be a polynomial of degree 1. yes no this function appears to have a positive leading coefficient. yes no this function appears to be g(x). yes no

Explanation:

Step1: Analyze the first graph

A degree 1 polynomial is a linear function (straight line). The first graph has a curve, not a straight line, so it's not a degree 1 polynomial. For leading coefficient: since it's not linear, but the curve's end behavior doesn't match linear. And about being \( g(x) \), assuming \( g(x) \) is linear (from context), it's not. So answers: No, No, No.

Step2: Analyze the second graph

It's a straight line, so degree 1 polynomial (Yes). The line has negative slope (going down from left to right), so leading coefficient (slope) is negative (No). If \( g(x) \) is, say, a linear function, but with negative slope, need to check context, but visually it's linear. So answers: Yes, No, (depends on \( g(x) \), but assuming \( g(x) \) is linear, maybe Yes if it matches, but from slope, leading coefficient is negative. Wait, the question is "This function appears to be \( g(x) \)" – without knowing \( g(x) \), but the graph is linear. Wait, maybe \( g(x) \) is linear. But the leading coefficient: slope is negative, so leading coefficient (for \( ax + b \), \( a \) is leading coefficient) is negative, so "This function appears to have a positive leading coefficient" is No.

Step3: Analyze the third graph

It's a curve (polynomial of higher degree, like cubic or quartic), not degree 1 (No). Leading coefficient: the right end goes up, so if it's a polynomial, the leading term's degree is even or odd? Wait, the graph has multiple turns, so degree at least 3? But the question is degree 1: No. Leading coefficient: if it's a polynomial, the right end going up – if degree is even, leading coefficient positive; but it's not degree 1. So "This function appears to have a positive leading coefficient" – but it's not degree 1, so first answer No. Then leading coefficient: maybe, but the function is not degree 1. And "This function appears to be \( g(x) \)" – \( g(x) \) is likely linear, so No.

But let's focus on the first sub - question for each graph:

First Graph:

• "This appears to be a polynomial of degree 1." A degree 1 polynomial is linear (straight line). The first graph is a curve (non - linear), so the answer is No.
• "This function appears to have a positive leading coefficient." Since it's not a linear polynomial, but the curve is decreasing (as x increases, y decreases), but for non - linear, leading coefficient of a polynomial is for the highest degree term. But since it's not degree 1, but if we consider the end behavior: as x approaches \(+\infty\), y approaches \(-\infty\), and as x approaches \(-\infty\), y approaches \(+\infty\) (wait, no, the first graph: left side, as x approaches the vertical line (asymptote?), no, it's a curve with a vertical asymptote? Wait, maybe it's a rational function, not a polynomial. So it's not a polynomial at all. So "polynomial of degree 1" is No.

Second Graph:

• "This appears to be a polynomial of degree 1." It's a straight line, so Yes (degree 1 polynomial is linear).
• "This function appears to have a positive leading coefficient." The slope (leading coefficient for linear \( y = mx + b \), \( m \) is leading coefficient) is negative (line goes down from left to right), so No.

Third Graph:

• "This appears to be a polynomial of degree 1." It's a curve (has multiple turning points), so No (degree 1 is linear, this is non - linear).

Answer:

First Graph:

• "This appears to be a polynomial of degree 1": No
• "This function appears to have a positive leading coefficient": No (assuming it's a non - polynomial, but if we consider as a polynomial, but it's not degree 1)
• "This function appears to be \( g(x) \)": No (assuming \( g(x) \) is linear)

Second Graph:

• "This appears to be a polynomial of degree 1": Yes
• "This function appears to have a positive leading coefficient": No
• "This function appears to be \( g(x) \)": (Depends on \( g(x) \), but if \( g(x) \) is linear, maybe Yes, but from slope, leading coefficient is negative)

Third Graph:

• "This appears to be a polynomial of degree 1": No
• "This function appears to have a positive leading coefficient": (Not applicable as it's not degree 1, but if we consider, the right end goes up, but it's not degree 1)
• "This function appears to be \( g(x) \)": No (assuming \( g(x) \) is linear)

But if we take the first question of each graph:

1. First Graph - "This appears to be a polynomial of degree 1": \(\boldsymbol{\text{No}}\)
2. Second Graph - "This appears to be a polynomial of degree 1": \(\boldsymbol{\text{Yes}}\)
3. Third Graph - "This appears to be a polynomial of degree 1": \(\boldsymbol{\text{No}}\)

For the "positive leading coefficient" questions:

1. First Graph: \(\boldsymbol{\text{No}}\) (non - linear, and end behavior shows decreasing)
2. Second Graph: \(\boldsymbol{\text{No}}\) (negative slope)
3. Third Graph: \(\boldsymbol{\text{No}}\) (not degree 1, so the question about positive leading coefficient for a degree 1 polynomial is not applicable, but the function is not degree 1)

For "This function appears to be \( g(x) \)":

1. First Graph: \(\boldsymbol{\text{No}}\) (non - linear)
2. Second Graph: \(\boldsymbol{\text{Yes}}\) (linear, matches \( g(x) \) if \( g(x) \) is linear)
3. Third Graph: \(\boldsymbol{\text{No}}\) (non - linear)

(Note: The answers for "This function appears to be \( g(x) \)" depend on the definition of \( g(x) \), but from the visual, the second graph is linear, so if \( g(x) \) is linear, it's a candidate. The first and third are non - linear, so No.)