Question

Consider the functions.

f(x)=4x^2
g(x)=15/4x^2
h(x)=4/15x^2

Answer 1

see the explanation

Explanation:

we know that

As the leading coefficient of the quadratic equation gets larger the parabola gets steeper and "narrower"

we have

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

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

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

Compare the leading coefficients

The leading coefficient of f(x) is 4

The leading coefficient of g(x) is 15/4=3.75

The leading coefficient of h(x) is 4/15=0.27

so

4> 3.75> 0.27

therefore

f(x) is steeper than g(x) and h(x)

g(x) is steeper than h(x)

Verify each statement

1) f(x) is steeper than h(x)

The statement is true

2) h(x) is steeper than g(x)

The statement is false

3) g(x) is steeper than f(x)

The statement is false