which function has a graph that is narrower than the graph of h(x)=x^2?
A graph of a function is said to be "narrower" if it is more vertically steep than another graph. For quadratic functions of the form f(x) = ax^2, where a is a real number, the graph will be narrower compared to the graph of h(x) = x^2 when the absolute value of the coefficient a is greater than 1.
For example, the graph of g(x) = 2x^2 is narrower than the graph of h(x) = x^2 because the coefficient 2 is greater than 1, which causes the graph of g(x) to increase or decrease more steeply than the graph of h(x).
Similarly, if you have a function like k(x) = -3x^2, the graph of k(x) will also be narrower than the graph of h(x) = x^2, even though the function opens downwards (because the coefficient is negative) — it's still steeper because the absolute value |-3| is greater than 1.