Question

Determine which function has the greatest rate of change as x approaches infinity.

A). f(x) = 2x − 8
B). g(x) = 5x2 − x + 7
C). h(x) = 4x − 6
D). There is not enough information to determine the answer.

Answer 1

Answer:  C). h(x) = 4x − 6

Step-by-step explanation:

all the others were incorrect

Answer 2

The function which has the greatest rate of change as x approaches infinity is g(x) = 5x2 − x + 7.

What is rate of change?

The rate of change of a function is the change in the value of one variable or quantity with respect to change in value of another variable.

The function given in the problem are,

• A). $f(x) = 2x - 8$
• B). $g(x) = 5x^2 -x + 7$
• C). $h(x) = 4x - 6$

It has to determine which function has the greatest rate of change as x approaches infinity. For this let a number, (say 5) and check the values of all the function on this number.

For the first function at x=5,

$f(5) = 2(5) - 8\\f(5) = 10 - 8\\f(5)=2$

For the second function at x=5,

$g(5) = 5(5)^2 -5 + 7\\g(5) = 125 -5 + 7\\g(5) = 127$

For the third function at x=5,

$h(5) = 4(5) - 6\\h(5) = 20 - 6\\h(5)=14$

Here, the value of the second function is greater when we compare the values of all the function.

Thus, the function which has the greatest rate of change as x approaches infinity is g(x) = 5x2 − x + 7.

Learn more about the rate of change here;

https://brainly.com/question/3939432