Mathematics

Problem

Which of the following statements correctly differentiates the basic shapes of the graphs of

y = x^4

and

y = x^5

? a) The graph of

y = x^4

is U-shaped and crosses the x-axis at the origin, whereas

y = x^5

is S-shaped and only touches the x-axis there. b) Both graphs are U-shaped and are symmetric about the y-axis. c) The graph of

y = x^4

is U-shaped and touches the x\text{-}axis at the origin, whereas the graph of

y = x^5

is S-shaped and crosses the x\text{-}axis at the origin. d) The graph of

y = x^4

is S-shaped, while the graph of

y = x^5

is U-shaped.