To determine which function has a graph that is narrower than the graph of h(x) = x^2, we need to look at the coefficient of the x^2 term in each of the given functions and compare it to the coefficient of the x^2 term in h(x).
A graph of a function f(x) = ax^2 will be narrower than the graph of h(x) = x^2 if the absolute value of the coefficient "a" is greater than 1. The wider or narrower aspect is due to the steepness of the parabola; larger values of "a" make the parabola open more steeply (narrower), while smaller absolute values of "a" result in a more gently opening parabola (wider).
Let's evaluate each option:
1. f(x) = x^2 - 9
Here the coefficient of the x^2 term is 1, which is the same as in h(x) = x^2. Therefore, the graph is not narrower; it's the same width but simply shifted downward by 9 units.
2. f(x) = -1.1x^2
Here the coefficient of the x^2 term is -1.1, which has an absolute value greater than 1. The negative sign indicates that the parabola opens downwards, but the fact that the absolute value of the coefficient is greater than 1 means the graph will be narrower than that of h(x).
3. f(x) = -0.1x^2
Here the coefficient of the x^2 term is -0.1, which has an absolute value less than 1. This means the graph will be wider than the graph of h(x), not narrower.
4. f(x) = x^2 + 3
Again, the coefficient of the x^2 term is 1, so this graph will have the same width as h(x) but will be shifted upward by 3 units.
Out of the options given, the graph of f(x) = -1.1x^2 is the one that is narrower than the graph of h(x) = x^2.
Which function has a graph that is narrower than the graph of h(x) = x^2?
Responses:
f(x) = x^2 - 9
f(x) = -1.1x^2
f(x) = -0.1x^2
f(x) = x^2 + 3
1 answer