Which of these will eventually have the greatest far of change compared to the others?
y=3x+10
y=2^2-3
y=x^2+8x+1 please
y=x^2+8x+1
In sorry I meant to write rate of change thank you
No problem! The rate of change for a linear function (such as y=3x+10) is constant, meaning it changes at a steady pace.
For the quadratic function y=x^2+8x+1, the rate of change is not constant since it is a curve, and its rate of change will vary at different points on the curve.
The exponential function y=2^2-3 increases rapidly as x increases, and its rate of change will also increase rapidly.
Therefore, the exponential function y=2^2-3 will eventually have the greatest rate of change compared to the linear and quadratic functions.
I thought you answered y=x^2+8x+1 not y=2^2-3?
My apologies for the oversight. Let's compare the rate of change for y = 3x + 10, y = x^2 + 8x + 1, and y = 2^x - 3.
1. y = 3x + 10: This is a linear function with a rate of change of 3. The rate of change remains constant as x changes.
2. y = x^2 + 8x + 1: This is a quadratic function with a changing rate of change. The rate of change increases as x increases.
3. y = 2^x - 3: This is an exponential function. The rate of change in an exponential function depends on the value of x. However, in general, exponential functions tend to have a rapid and increasing rate of change as x increases.
Based on this analysis, the exponential function y = 2^x - 3 will eventually have the greatest rate of change compared to the linear and quadratic functions.