Question

3. The points (0, 1) and (1,2) lie on all three of a linear, an exponential, and a quadratic function.

All three functions are always increasing when x > 0.
The functions are:
Linear: y = x+1,
Exponential: y = 2*,
Quadratic: y = x2 +1
Which of these three functions will be greatest in value when x = 10? Explain your reasoning.

Answer 1

exponential

Explanation:

The exponential function has the largest value for large values of x. Here, "large" means "greater than 4.3". A graph shows this to be true.

For x=10, the exponential function will have a value of 2^10 = 1024.

The quadratic function will have a value of 10^2+1 = 101.

The linear function will have a value of 10+1 = 11.

The exponential function has the largest value.