Question

f(x) = -4x - 8

first image (left):
this appears to be a polynomial of degree 3.
yes no
this function appears to have a negative leading coefficient.
yes no
this function appears to be f(x).
yes no

second image (middle):
this appears to be a polynomial of degree 3.
yes no
this function appears to have a negative leading coefficient.
yes no
this function appears to be f(x).
yes no

third image (right):
this appears to be a polynomial of degree 3.
yes no
this function appears to have a negative leading coefficient.
yes no
this function appears to be f(x).
yes no

Explanation:

Step1: Analyze the function \( f(x) = -4x - 8 \)

The function \( f(x) = -4x - 8 \) is a linear function (degree 1), not a degree 3 polynomial. Also, its graph is a straight line with a negative slope (leading coefficient -4, negative).

Step2: Analyze the first graph

• "This appears to be a polynomial of degree 3": The first graph is a parabola - like (degree 2), not degree 3. So answer "No".
• "This function appears to have a negative leading coefficient": The parabola opens upwards, so leading coefficient positive. Answer "No".
• "This function appears to be \( f(x) \)": \( f(x) \) is linear, this is a parabola. Answer "No".

Step3: Analyze the second graph

• "This appears to be a polynomial of degree 3": The second graph is a parabola (degree 2), not degree 3. Answer "No".
• "This function appears to have a negative leading coefficient": The parabola opens upwards, leading coefficient positive. Answer "No".
• "This function appears to be \( f(x) \)": \( f(x) \) is linear, this is a parabola. Answer "No".

Step4: Analyze the third graph

• "This appears to be a polynomial of degree 3": The third graph is a straight line (degree 1), not degree 3. Answer "No".
• "This function appears to have a negative leading coefficient": The line has a negative slope (goes down from left to right), so leading coefficient (slope) is -4 (negative). Answer "Yes".
• "This function appears to be \( f(x) \)": \( f(x) = -4x - 8 \) is a linear function with negative slope, this graph is a straight line with negative slope. Answer "Yes".

Answer:

First Graph:

• "This appears to be a polynomial of degree 3": No
• "This function appears to have a negative leading coefficient": No
• "This function appears to be \( f(x) \)": No

Second Graph:

• "This appears to be a polynomial of degree 3": No
• "This function appears to have a negative leading coefficient": No
• "This function appears to be \( f(x) \)": No

Third Graph:

• "This appears to be a polynomial of degree 3": No
• "This function appears to have a negative leading coefficient": Yes
• "This function appears to be \( f(x) \)": Yes