Polynomial function compared to an Exponential function

Question

Given a polynomial function f(x) = 2x² + 7x + 6 and an exponential function g(x) = 2^x + 5, what key features do f(x) and g(x) have in common?

 Both f(x) and g(x) increase over the interval of [–4 , ∞)

 Both f(x) and g(x) have the same x-intercepts of (–2, 0) and (–1.5, 0). 

Both f(x) and g(x) have the same y-intercept of (0, 6). 

Both f(x) and g(x) have the same range of (–∞, 0].

Answer 1

Hey!

First things first, it's easier to compare two functions if you can compare them by graphs.

The first function is a polynomial function - try your best to put these in standard form so that you can see where the roots/x-intercepts are. You can set the function equal to zero to find the roots, as well as set x=0 to find the y-intercept.

The second function is an exponential function. These always diverge ("shoot off") to positive infinity on the y-axis, and are asymptotic on the x axis, diverging to negative infinity. The only difference is made by a +5 here...that is a ENTIRE vertical shift up of 5 units! Exponential functions also have a special y-intercept...think about what will happen if this intercept is shifted up 5 units!

Know the forms of these two functions and how to graph them and it will make them much easier to compare.