Please verify your account before proceeding.
Which graph represents the function 𝑦 = −2.5𝑥³ + 3?
Which graph represents the function 𝑦 equals negative 2.5 𝑥 cubed plus three?
A cubic function is a function where the greatest power of a variable is three. If the leading coefficient of a cubic function, meaning the number in front of the first term which it would be an 𝑥 cubed, if it is positive, our graph will be increasing left or right, so going up. And if there would be a negative leading coefficient — the number in front of 𝑥 cubed, the first term 𝑥 cubed — then our graph would be decreasing left or right, it will be going down. Therefore, since we already know that it’s a cubic function and we have a negative leading coefficient, negative 2.5, our graph should be decreasing left or right. So we can go ahead and eliminate options a and b because these are increasing left or right.
Now notice, it is 𝑦 equals negative 2.5 𝑥 cubed plus three. And our last two options c and d, we have our graph crossing the 𝑦-axis at positive three for c and our graph crossing the 𝑦 axis at negative three for option d. Since we want to be crossing the 𝑦-axis at positive three, our correct answer would be graph c.
So graph c represents the function 𝑦 equals negative 2.5 𝑥 cubed plus three.
To further our thinking about this question, let’s talk about why some of the graphs look a little different than the others. When the coefficient of 𝑥 cubed is greater in magnitude, then as the 𝑥-coordinates increase, the 𝑦 coordinates increase faster and the curve accelerates away from the 𝑥-axis at a faster rate. Obviously, both curves extend infinitely in the positive and negative 𝑥-directions. But for these limited snapshots of the curve, that makes the curve look thinner. While this information doesn’t change our answer, it’s just something to keep in mind.
Don’t have an account? Sign Up