The graphs can be matched to the equations as follows:
R: F(x) = 3x^5 - 3x^2 + 4x + 2
S: G(x) = 3x^3
U: F(x) = 1/2x^2
T: F(x) = x^3 - 8
V: F(x) = 4x^4 - 3x^3 + 4x
The graphs can be matched to the equations as follows:
F(x) = 3x^5 - 3x^2 + 4x + 2: This equation is a quintic function, which means it has a degree of 5. The graph of a quintic function with positive leading coefficient will typically have an upward curve at both ends and a downward curve in the middle. Looking at the graphs, the graph in box R most closely matches this description.
G(x) = 3x^3: This equation is a cubic function, which means it has a degree of 3. The graph of a cubic function with positive leading coefficient will typically have an upward curve at one end and a downward curve at the other. Looking at the graphs, the graph in box S most closely matches this description.
F(x) = 1/2x^2: This equation is a quadratic function, which means it has a degree of 2. The graph of a quadratic function with positive leading coefficient will be a U-shaped curve. Looking at the graphs, the graph in box U most closely matches this description.
F(x) = x^3 - 8: This equation is a cubic function, but with a negative leading coefficient. The graph of a cubic function with negative leading coefficient will be the opposite of a cubic function with positive leading coefficient, meaning it will have a downward curve at one end and an upward curve at the other. Looking at the graphs, the graph in box T most closely matches this description.
F(x) = 4x^4 - 3x^3 + 4x: This equation is a quartic function, which means it has a degree of 4. The graph of a quartic function can have a variety of shapes, depending on the coefficients of the equation. However, the graph in box V has the most extreme features of the graphs in the answer choices, so it is the most likely match.