Question

Let f(x)=x2+3x−4 .

Answer 1

Answer:

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

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Answer 2

Answer:

1) The average rate of change is 8.

2) The average rate of change is 112.

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

Step-by-step 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 $A_v=\frac{f(b)-f(a)}{b-a}$

Where, a=-3 and b=8

$A_v=\frac{((8)^2+3(8)-4)-((-3)^2+3(-3)-4)}{8-(-3)}$

$A_v=\frac{(84)-(-4)}{11}$

$A_v=\frac{88}{11}$

$A_v=8$

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 $A_v=\frac{f(b)-f(a)}{b-a}$

Where, a=-2 and b=2

$A_v=\frac{(-14(2+4)^2-8)-(-14(-2+4)^2-8)}{-2-2}$

$A_v=\frac{(-512)-(-64)}{-4}$

$A_v=\frac{-448}{-4}$

$A_v=112$

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.