Question

Which of the following graphs represents a function that has a positive leading coefficient? Check all that apply.

Answer 1

Alright, so i'm looking at the graphs and i'm seeing B as an answer, Probably not A. C and D are confusing,

In the end, i'd say B and D.

If i'm wrong, please tell me.

Answer 2

The correct answers are (B), (C), and (D).

(C) is pretty straight forward. The graph resembles the graph of a quadratic function that us concave upwards. A quadratic function, and functions with an even degree like
`x^4, x^6` will be concave upwards if the leading term is positive.

For function with an odd degree such as
`x^3, x^5` will be mostly negative on the side of the negative x axis and positive on the side of the positive x-axis if the leading coefficient is positive. A cubic function with a positive leading term will be negative on the side of the negative x-axis for large negative numbers and positive on the side of the positive x-axis for large positive numbers. From this explaination we can gather that (B) and (D) are also correct .

The correct options are (B),(C) and (D).