Question

Consider the functions.

f(x)=4x2
g(x)=154x2
h(x)=415x2

How do the graphs of these function compare to one another?

Select True or False for each statement.

Answer 1

true false false

Explanation:

Answer 2

The answers for the three statements are true, false and false.

Explanation:

The steepness of a curve is measured by the slope of that curve.

We are given three parabolic curves of the form y = k
`x^(2)`

The slope at each point would depend on the k term.

So the curve with higher value of k will be having higher slope and the curve will be steeper.

f(x) = 4
`x^(2)`

g(x) =
`(15)/(4) x^(2)`

h(x) =
`(4)/(15) x^(2)`

(a)f(x) is steeper than h(x) because k value is higher for f(x).

(b)h(x) is not steeper than g(x).

(c)g(x) is not steeper than f(x) because the k value is lesser.