Question

this appears to be? yes no the degree of this function appears to be? yes no this function appears to be f(x). yes no this appears to be a cubic function. yes no the degree of this function appears to be even. yes no this function appears to be f(x). yes no this appears to be a cubic function. yes no the degree of this function appears to be even. yes no this function appears to be f(x). yes no

Explanation:

Step1: Analyze the first graph

The first graph has a symmetric shape about the y - axis, which is characteristic of an even - degree function (like a parabola, degree 2). A cubic function has degree 3 (odd), so this is not a cubic function. So for "This appears to be a cubic function", the answer is No. For "The degree of this function appears to be even", since it is symmetric about the y - axis, the degree is even, so the answer is Yes. For "This function appears to be \(f(x)\)" (assuming \(f(x)\) is a non - cubic function), if \(f(x)\) is not cubic, then if the graph is not cubic, we need to check. But from the shape, it's even - degree, not cubic.

Step2: Analyze the second graph

The second graph has a single "hump" and the end - behaviors: as \(x\to-\infty\), the function goes to \(+\infty\) and as \(x\to+\infty\), it goes to \(-\infty\) (or vice - versa depending on the leading coefficient), which is characteristic of a cubic function (degree 3, odd). So "This appears to be a cubic function" is Yes. A cubic function has an odd degree, so "The degree of this function appears to be even" is No. For "This function appears to be \(f(x)\)", if \(f(x)\) is cubic, then this could be yes.

Step3: Analyze the third graph

The third graph has end - behaviors that are both going to the same direction (both to \(+\infty\) or both to \(-\infty\))? Wait, no, looking at the graph, as \(x\to-\infty\) and \(x\to+\infty\), the function has end - behaviors consistent with an even - degree function? Wait, no, the third graph: let's check the shape. Wait, the third graph's end - behaviors: if it's a cubic, the end - behaviors should be opposite. Wait, maybe I misread. Wait, the third graph: the curve is increasing on both ends? No, maybe the first graph: symmetric about y - axis (even function, degree 2), second graph: cubic (degree 3, odd, with one local max and one local min), third graph: let's see, the third graph's end - behaviors: as \(x\to-\infty\) and \(x\to+\infty\), if it's a cubic, the leading coefficient's sign determines the end - behaviors. But the third graph: if we assume the function \(f(x)=-x^{3}+12x^{2}-48x + 56\), let's find its degree: degree 3 (cubic). Let's find its end - behaviors: the leading term is \(-x^{3}\), so as \(x\to+\infty\), \(f(x)\to-\infty\) and as \(x\to-\infty\), \(f(x)\to+\infty\). The second graph has end - behaviors that match this (as \(x\to-\infty\), up; as \(x\to+\infty\), down), which is a cubic with negative leading coefficient. The third graph: as \(x\to-\infty\) and \(x\to+\infty\), if it's going to the same direction, it's even - degree. But the function \(f(x)\) is cubic, so the second graph is cubic.

Answer:

For the first graph:

• This appears to be a cubic function: No
• The degree of this function appears to be even: Yes
• This function appears to be \(f(x)\): (Depends on \(f(x)\), but from shape, if \(f(x)\) is not cubic, No)

For the second graph:

• This appears to be a cubic function: Yes
• The degree of this function appears to be even: No
• This function appears to be \(f(x)\): (If \(f(x)\) is cubic, Yes)

For the third graph:

• This appears to be a cubic function: No (if end - behaviors are same, even - degree)
• The degree of this function appears to be even: Yes (if end - behaviors are same)
• This function appears to be \(f(x)\): No (if \(f(x)\) is cubic)

(Assuming the function \(f(x)=-x^{3}+12x^{2}-48x + 56\) is cubic, the second graph is the cubic one, so for the second graph: "This appears to be a cubic function" - Yes, "The degree of this function appears to be even" - No, "This function appears to be \(f(x)\)" - Yes (if \(f(x)\) is this cubic))