Question

Let f(x)=x2+3x−4 .

What is the average rate of change for the quadratic function from x=−3 to x = 8?


Let f(x)=−14(x+4)2−8 .

What is the average rate of change for the quadratic function from x=−2 to x = 2?


Which function grows at the fastest rate for increasing values of x?



f(x)=4⋅2x

h(x)=9x2+25

g(x)=15x+6

Answer 1

f(x) = 4 · 2^x is the correct answer for Which function grows at the fastest rate for increasing values of x?

I included a screenshot so u can see.

Hope this helps!

Answer 2

1) The average rate of change is 8.

2) The average rate of change is 112.

3) f(x) grows at the fastest rate.

Explanation:

1) Given : Function
`f(x)=x^2+3x-4`

To find : What is the average rate of change for the quadratic function from x=−3 to x = 8?

Solution :

The average rate of change is
`A_v=(f(b)-f(a))/(b-a)`

Where, a=-3 and b=8

`A_v=(((8)^2+3(8)-4)-((-3)^2+3(-3)-4))/(8-(-3))`

`A_v=((84)-(-4))/(11)`

`A_v=(88)/(11)`

`A_v=8`

The average rate of change is 8.

2) Given : Function
`f(x)=-14(x+4)^2-8`

To find : What is the average rate of change for the quadratic function from x=−2 to x = 2?

Solution :

The average rate of change is
`A_v=(f(b)-f(a))/(b-a)`

Where, a=-2 and b=2

`A_v=((-14(2+4)^2-8)-(-14(-2+4)^2-8))/(-2-2)`

`A_v=((-512)-(-64))/(-4)`

`A_v=(-448)/(-4)`

`A_v=112`

The average rate of change is 112.

3) To find : Which function grows at the fastest rate for increasing values of x?

Solution :

1)
`f(x)=4\cdot2^x` is an exponential function.

2)
`h(x)=9x^2+25` is a quadratic function.

3)
`g(x)=15x+6` is a linear function.

Increasing values of x will increase exponentially.

So, it will grow at the fastest rate.

f(x) grows at the fastest rate.